Prompt:
Given:
p1: 2 is divisible by 3.
p2: 7 is considered lucky.
p3: Pi is odd.

Symbolize the following propositions using &, ||, ~:
(1) Pi is odd. and 2 is divisible by 3. and p2=>p1
(2) It is not the case that It is not the case that Pi is odd.
(3) 7 is considered lucky. and p3=>p2 and 7 is considered lucky.
(4) It is not the case that 7 is considered lucky. and Pi is odd.

Format your answers as [[...];[...];...]

Answer: ((p3&p1)&(p2=>p1))

Answer: ~~p3

Answer: ((p2&p3)=>(p2&p2))

Answer: ~(p2&p3)


Prompt:
Given:
p1: Blue is a prime number.
p2: 2 is a prime number.
p3: Pi is even.

Symbolize the following propositions using &, ||, ~:
(1) Blue is a prime number. or Pi is even. and Pi is even. and Pi is even.
(2) It is not the case that Blue is a prime number. and Pi is even.
(3) It is not the case that It is not the case that 2 is a prime number.

Format your answers as [[...];[...];...]

Answer: ((p1||p3)&(p3&p3))

Answer: ~(p1&p3)

Answer: ~~p2


Prompt:
Given:
p1: Pi is odd.
p2: 7 is a fruit.
p3: Blue is a fruit.

Symbolize the following propositions using &, ||, ~:
(1) Pi is odd. or 7 is a fruit. or Pi is odd. or 7 is a fruit.
(2) It is not the case that 7 is a fruit. or It is not the case that Blue is a fruit.
(3) It is not the case that Pi is odd. or Blue is a fruit.

Format your answers as [[...];[...];...]

Answer: ((p1||p2)||(p1||p2))

Answer: (~p2||~p3)

Answer: ~(p1||p3)


Prompt:
Given:
p1: 5 is divisible by 3.
p2: 4 is a prime number.
p3: 7 is a fruit.
p4: Red is considered lucky.

Symbolize the following propositions using &, ||, ~:
(1) p4=>p3 or 7 is a fruit. or 5 is divisible by 3.
(2) p3=p2=p3 and Red is considered lucky.
(3) It is not the case that p4=>p2=>p3

Format your answers as [[...];[...];...]

Answer: ((p4=>p3)||(p3||p1))

Answer: ((p3=p2)=(p3&p4))

Answer: (~p4=>(p2=>p3))


Prompt:
Given:
p1: 2 is divisible by 3.
p2: Red is odd.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that Red is odd. and It is not the case that 2 is divisible by 3.
(2) 2 is divisible by 3. or 2 is divisible by 3. or It is not the case that 2 is divisible by 3.
(3) It is not the case that 2 is divisible by 3. and 2 is divisible by 3.
(4) It is not the case that Red is odd. or It is not the case that Red is odd.
(5) It is not the case that Red is odd. and 2 is divisible by 3.

Format your answers as [[...];[...];...]

Answer: (~p2&~p1)

Answer: ((p1||p1)||~p1)

Answer: ~(p1&p1)

Answer: (~p2||~p2)

Answer: ~(p2&p1)


Prompt:
Given:
p1: Blue is even.
p2: 5 is even.
p3: 2 is divisible by 3.
p4: 4 is considered lucky.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that 2 is divisible by 3. or 5 is even.
(2) 4 is considered lucky. and p2= It is not the case that 4 is considered lucky.
(3) 4 is considered lucky. and p3=>p4=p4

Format your answers as [[...];[...];...]

Answer: ~(p3||p2)

Answer: ((p4&p2)=~p4)

Answer: ((p4&p3)=>(p4=p4))


Prompt:
Given:
p1: Blue is considered lucky.
p2: Pi is considered lucky.
p3: Square root of 3 is a common color.
p4: 7 is divisible by 3.

Symbolize the following propositions using &, ||, ~:
(1) 7 is divisible by 3. and Blue is considered lucky. and p4=p2
(2) p1=p2 and p4=p3
(3) p1=>p4= It is not the case that Square root of 3 is a common color.

Format your answers as [[...];[...];...]

Answer: ((p4&p1)&(p4=p2))

Answer: ((p1=p2)&(p4=p3))

Answer: ((p1=>p4)=~p3)


Prompt:
Given:
p1: 5 is odd.
p2: 4 is a fruit.
p3: Pi is divisible by 3.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that 4 is a fruit. and 4 is a fruit. or 5 is odd.
(2) It is not the case that Pi is divisible by 3. or 4 is a fruit.
(3) 5 is odd. or 4 is a fruit. and It is not the case that 5 is odd.

Format your answers as [[...];[...];...]

Answer: (~p2&(p2||p1))

Answer: ~(p3||p2)

Answer: ((p1||p2)&~p1)


Prompt:
Given:
p1: 4 is even.
p2: 2 is a fruit.
p3: Pi is divisible by 3.

Symbolize the following propositions using &, ||, ~:
(1) 4 is even. and p1=>p1 and Pi is divisible by 3.
(2) p3=>p2=>p3=>p3
(3) p2=>p1 and Pi is divisible by 3. and 2 is a fruit.
(4) p3=>p2 and It is not the case that Pi is divisible by 3.

Format your answers as [[...];[...];...]

Answer: ((p1&p1)=>(p1&p3))

Answer: ((p3=>p2)=>(p3=>p3))

Answer: ((p2=>p1)&(p3&p2))

Answer: ((p3=>p2)&~p3)


Prompt:
Given:
p1: Red is a fruit.
p2: Blue is divisible by 3.
p3: 7 is even.

Symbolize the following propositions using &, ||, ~:
(1) 7 is even. or 7 is even. and It is not the case that Red is a fruit.
(2) Blue is divisible by 3. or Red is a fruit. and Blue is divisible by 3. and Red is a fruit.
(3) 7 is even. and Blue is divisible by 3. or It is not the case that 7 is even.

Format your answers as [[...];[...];...]

Answer: ((p3||p3)&~p1)

Answer: ((p2||p1)&(p2&p1))

Answer: ((p3&p2)||~p3)


Prompt:
Given:
p1: Square root of 3 is odd.
p2: 5 is divisible by 3.
p3: 2 is considered lucky.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that 5 is divisible by 3. and It is not the case that Square root of 3 is odd.
(2) 2 is considered lucky. and 5 is divisible by 3. and 2 is considered lucky. and 2 is considered lucky.
(3) 5 is divisible by 3. and 5 is divisible by 3. and It is not the case that Square root of 3 is odd.

Format your answers as [[...];[...];...]

Answer: (~p2&~p1)

Answer: ((p3&p2)&(p3&p3))

Answer: ((p2&p2)&~p1)


Prompt:
Given:
p1: Square root of 3 is a common color.
p2: 5 is a prime number.
p3: 4 is a common color.
p4: Red is even.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that p4=> It is not the case that 5 is a prime number.
(2) p1=>p4=p1=p1
(3) 4 is a common color. or p4=p2=>p1

Format your answers as [[...];[...];...]

Answer: (~p4=>~p2)

Answer: ((p1=>p4)=(p1=p1))

Answer: ((p3||p4)=(p2=>p1))


Prompt:
Given:
p1: 4 is a prime number.
p2: 5 is a prime number.

Symbolize the following propositions using &, ||, ~:
(1) 5 is a prime number. or 5 is a prime number. or It is not the case that 4 is a prime number.
(2) 5 is a prime number. and 5 is a prime number. or It is not the case that 5 is a prime number.
(3) It is not the case that 5 is a prime number. and 4 is a prime number.
(4) It is not the case that 4 is a prime number. or It is not the case that 5 is a prime number.
(5) 5 is a prime number. or 5 is a prime number. or It is not the case that 5 is a prime number.

Format your answers as [[...];[...];...]

Answer: ((p2||p2)||~p1)

Answer: ((p2&p2)||~p2)

Answer: ~(p2&p1)

Answer: (~p1||~p2)

Answer: ((p2||p2)||~p2)


Prompt:
Given:
p1: Blue is considered lucky.
p2: Red is odd.
p3: 2 is odd.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that It is not the case that 2 is odd.
(2) It is not the case that p2=> It is not the case that 2 is odd.
(3) p2=>p1=>p1 and 2 is odd.
(4) It is not the case that It is not the case that Red is odd.

Format your answers as [[...];[...];...]

Answer: ~~p3

Answer: (~p2=>~p3)

Answer: ((p2=>p1)=>(p1&p3))

Answer: ~~p2


Prompt:
Given:
p1: 2 is divisible by 3.
p2: Blue is a prime number.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that 2 is divisible by 3. and Blue is a prime number.
(2) It is not the case that 2 is divisible by 3. or Blue is a prime number.
(3) It is not the case that It is not the case that 2 is divisible by 3.
(4) It is not the case that 2 is divisible by 3. or It is not the case that Blue is a prime number.
(5) 2 is divisible by 3. and Blue is a prime number. and 2 is divisible by 3. or 2 is divisible by 3.

Format your answers as [[...];[...];...]

Answer: ~(p1&p2)

Answer: ~(p1||p2)

Answer: ~~p1

Answer: (~p1||~p2)

Answer: ((p1&p2)&(p1||p1))


Prompt:
Given:
p1: Pi is a fruit.
p2: Red is odd.
p3: 2 is even.
p4: 5 is divisible by 3.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that p4=p2=>p4
(2) 5 is divisible by 3. and Pi is a fruit. or p4=p2
(3) It is not the case that 5 is divisible by 3. or 2 is even.

Format your answers as [[...];[...];...]

Answer: (~p4=(p2=>p4))

Answer: ((p4&p1)||(p4=p2))

Answer: ~(p4||p3)


Prompt:
Given:
p1: Square root of 3 is divisible by 3.
p2: Blue is a common color.
p3: 2 is divisible by 3.

Symbolize the following propositions using &, ||, ~:
(1) p1=>p3=>p3=>p3
(2) It is not the case that It is not the case that 2 is divisible by 3.
(3) p2=>p3=> It is not the case that 2 is divisible by 3.
(4) Blue is a common color. and Square root of 3 is divisible by 3. and p2=>p3

Format your answers as [[...];[...];...]

Answer: ((p1=>p3)=>(p3=>p3))

Answer: ~~p3

Answer: ((p2=>p3)=>~p3)

Answer: ((p2&p1)&(p2=>p3))


Prompt:
Given:
p1: Red is a fruit.
p2: Square root of 3 is odd.
p3: 7 is a common color.

Symbolize the following propositions using &, ||, ~:
(1) Square root of 3 is odd. and 7 is a common color. or 7 is a common color. and Square root of 3 is odd.
(2) It is not the case that Square root of 3 is odd. or Square root of 3 is odd.
(3) It is not the case that It is not the case that Square root of 3 is odd.

Format your answers as [[...];[...];...]

Answer: ((p2&p3)||(p3&p2))

Answer: ~(p2||p2)

Answer: ~~p2


Prompt:
Given:
p1: 4 is a common color.
p2: 2 is a prime number.
p3: Square root of 3 is a prime number.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that Square root of 3 is a prime number. and 2 is a prime number.
(2) It is not the case that It is not the case that Square root of 3 is a prime number.
(3) p1=>p1 and It is not the case that 4 is a common color.
(4) p1=>p1 and It is not the case that Square root of 3 is a prime number.

Format your answers as [[...];[...];...]

Answer: ~(p3&p2)

Answer: ~~p3

Answer: ((p1=>p1)&~p1)

Answer: ((p1=>p1)&~p3)


Prompt:
Given:
p1: Red is a fruit.
p2: 7 is even.
p3: Blue is a prime number.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that 7 is even. or Red is a fruit. and Red is a fruit.
(2) Blue is a prime number. or Blue is a prime number. and 7 is even. or Blue is a prime number.
(3) Blue is a prime number. and 7 is even. and Red is a fruit. or Red is a fruit.

Format your answers as [[...];[...];...]

Answer: (~p2||(p1&p1))

Answer: ((p3||p3)&(p2||p3))

Answer: ((p3&p2)&(p1||p1))


Prompt:
Given:
p1: Red is even.
p2: 7 is considered lucky.
p3: Square root of 3 is even.
p4: Pi is divisible by 3.

Symbolize the following propositions using &, ||, ~:
(1) Red is even. or p1=>p3=>p2
(2) It is not the case that p4=p1
(3) Pi is divisible by 3. or Pi is divisible by 3. or p4=p1

Format your answers as [[...];[...];...]

Answer: ((p1||p1)=>(p3=>p2))

Answer: ~(p4=p1)

Answer: ((p4||p4)||(p4=p1))


Prompt:
Given:
p1: 4 is considered lucky.
p2: Pi is odd.

Symbolize the following propositions using &, ||, ~:
(1) Pi is odd. and Pi is odd. or Pi is odd. or Pi is odd.
(2) Pi is odd. and Pi is odd. or It is not the case that Pi is odd.
(3) 4 is considered lucky. and 4 is considered lucky. and Pi is odd. and 4 is considered lucky.
(4) 4 is considered lucky. and 4 is considered lucky. or Pi is odd. and 4 is considered lucky.
(5) It is not the case that Pi is odd. or Pi is odd.

Format your answers as [[...];[...];...]

Answer: ((p2&p2)||(p2||p2))

Answer: ((p2&p2)||~p2)

Answer: ((p1&p1)&(p2&p1))

Answer: ((p1&p1)||(p2&p1))

Answer: ~(p2||p2)


Prompt:
Given:
p1: 5 is divisible by 3.
p2: Blue is a common color.
p3: 7 is a common color.
p4: 2 is odd.

Symbolize the following propositions using &, ||, ~:
(1) p1=>p2=> It is not the case that 2 is odd.
(2) p2=>p4=>p4 and 7 is a common color.
(3) p1=p1=>p1 and Blue is a common color.

Format your answers as [[...];[...];...]

Answer: ((p1=>p2)=>~p4)

Answer: ((p2=>p4)=>(p4&p3))

Answer: ((p1=p1)=>(p1&p2))


Prompt:
Given:
p1: 2 is even.
p2: Square root of 3 is divisible by 3.
p3: Blue is divisible by 3.
p4: 4 is divisible by 3.

Symbolize the following propositions using &, ||, ~:
(1) p4=p3=>p4=p4
(2) p3=>p4=> It is not the case that Square root of 3 is divisible by 3.
(3) Square root of 3 is divisible by 3. or p4= It is not the case that 4 is divisible by 3.

Format your answers as [[...];[...];...]

Answer: ((p4=p3)=>(p4=p4))

Answer: ((p3=>p4)=>~p2)

Answer: ((p2||p4)=~p4)


Prompt:
Given:
p1: Pi is divisible by 3.
p2: 5 is divisible by 3.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that Pi is divisible by 3. or 5 is divisible by 3. and Pi is divisible by 3.
(2) Pi is divisible by 3. and Pi is divisible by 3. or It is not the case that Pi is divisible by 3.
(3) It is not the case that 5 is divisible by 3. or 5 is divisible by 3.
(4) Pi is divisible by 3. or 5 is divisible by 3. and Pi is divisible by 3. or 5 is divisible by 3.
(5) Pi is divisible by 3. or Pi is divisible by 3. and Pi is divisible by 3. or 5 is divisible by 3.

Format your answers as [[...];[...];...]

Answer: (~p1||(p2&p1))

Answer: ((p1&p1)||~p1)

Answer: ~(p2||p2)

Answer: ((p1||p2)&(p1||p2))

Answer: ((p1||p1)&(p1||p2))


Prompt:
Given:
p1: Pi is odd.
p2: Square root of 3 is odd.
p3: 2 is a common color.

Symbolize the following propositions using &, ||, ~:
(1) Pi is odd. and 2 is a common color. and p2=>p3
(2) Square root of 3 is odd. and p3=>p2=>p2
(3) It is not the case that p2=>p1
(4) 2 is a common color. and Square root of 3 is odd. and p3=>p2

Format your answers as [[...];[...];...]

Answer: ((p1&p3)&(p2=>p3))

Answer: ((p2&p3)=>(p2=>p2))

Answer: ~(p2=>p1)

Answer: ((p3&p2)&(p3=>p2))


Prompt:
Given:
p1: 5 is considered lucky.
p2: Pi is a prime number.
p3: Red is a common color.
p4: 4 is divisible by 3.

Symbolize the following propositions using &, ||, ~:
(1) p3=p3=>p2=>p2
(2) It is not the case that p3=>p3=>p1
(3) It is not the case that p2=>p2=p2

Format your answers as [[...];[...];...]

p3=p3=>p2=>p2
It is not the case that p3=>p3=>p1
It is not the case that p2=>p2=p2

Answer: ((p3=p3)=>(p2=>p2))

Answer: (~p3=>(p3=>p1))

Answer: (~p2=>(p2=p2))


Prompt:
Given:
p1: 5 is odd.
p2: 7 is considered lucky.
p3: Blue is odd.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that Blue is odd. and p2=>p2
(2) 5 is odd. and p3=>p2=>p3
(3) p1=>p1=>p1 and 7 is considered lucky.
(4) 7 is considered lucky. and 5 is odd. and p2=>p3

Format your answers as [[...];[...];...]

Answer: (~p3&(p2=>p2))

Answer: ((p1&p3)=>(p2=>p3))

Answer: ((p1=>p1)=>(p1&p2))

Answer: ((p2&p1)&(p2=>p3))


Prompt:
Given:
p1: Blue is even.
p2: 4 is odd.
p3: 7 is odd.
p4: Pi is a prime number.

Symbolize the following propositions using &, ||, ~:
(1) p3=p3 and 4 is odd. and 4 is odd.
(2) 7 is odd. or 7 is odd. or It is not the case that Blue is even.
(3) p2=p3 or Pi is a prime number. or 4 is odd.

Format your answers as [[...];[...];...]

Answer: ((p3=p3)&(p2&p2))

Answer: ((p3||p3)||~p1)

Answer: ((p2=p3)||(p4||p2))


Prompt:
Given:
p1: 5 is a common color.
p2: Red is a common color.
p3: Square root of 3 is a common color.

Symbolize the following propositions using &, ||, ~:
(1) p1=>p1 and It is not the case that Red is a common color.
(2) It is not the case that It is not the case that Red is a common color.
(3) It is not the case that p3=>p3=>p3
(4) It is not the case that p2=>p1

Format your answers as [[...];[...];...]

Answer: ((p1=>p1)&~p2)

Answer: ~~p2

Answer: (~p3=>(p3=>p3))

Answer: ~(p2=>p1)


Prompt:
Given:
p1: Red is odd.
p2: Blue is divisible by 3.
p3: 5 is divisible by 3.

Symbolize the following propositions using &, ||, ~:
(1) 5 is divisible by 3. or Blue is divisible by 3. and It is not the case that 5 is divisible by 3.
(2) Red is odd. or Blue is divisible by 3. or Blue is divisible by 3. or 5 is divisible by 3.
(3) 5 is divisible by 3. and 5 is divisible by 3. and It is not the case that 5 is divisible by 3.

Format your answers as [[...];[...];...]

Answer: ((p3||p2)&~p3)

Answer: ((p1||p2)||(p2||p3))

Answer: ((p3&p3)&~p3)


Prompt:
Given:
p1: Red is even.
p2: 2 is considered lucky.
p3: Pi is even.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that It is not the case that 2 is considered lucky.
(2) 2 is considered lucky. or Red is even. or Red is even. and Red is even.
(3) It is not the case that It is not the case that Red is even.

Format your answers as [[...];[...];...]

Answer: ~~p2

Answer: ((p2||p1)||(p1&p1))

Answer: ~~p1


Prompt:
Given:
p1: 7 is a common color.
p2: Blue is odd.
p3: Red is a fruit.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that 7 is a common color. or It is not the case that Blue is odd.
(2) Blue is odd. and Blue is odd. and It is not the case that 7 is a common color.
(3) Red is a fruit. and Red is a fruit. and It is not the case that Blue is odd.

Format your answers as [[...];[...];...]

Answer: (~p1||~p2)

Answer: ((p2&p2)&~p1)

Answer: ((p3&p3)&~p2)


Prompt:
Given:
p1: Red is even.
p2: 7 is a common color.
p3: Blue is divisible by 3.
p4: Pi is divisible by 3.

Symbolize the following propositions using &, ||, ~:
(1) Pi is divisible by 3. and p3= It is not the case that Pi is divisible by 3.
(2) It is not the case that Red is even. and p4=p4
(3) Pi is divisible by 3. and p3=>p4=>p3

Format your answers as [[...];[...];...]

Answer: ((p4&p3)=~p4)

Answer: (~p1&(p4=p4))

Answer: ((p4&p3)=>(p4=>p3))


Prompt:
Given:
p1: Blue is divisible by 3.
p2: 4 is odd.
p3: Red is a fruit.
p4: Square root of 3 is a common color.

Symbolize the following propositions using &, ||, ~:
(1) 4 is odd. or p2=p4 and Blue is divisible by 3.
(2) It is not the case that p4=p2=>p3
(3) p4=>p2 or Blue is divisible by 3. and Square root of 3 is a common color.

Format your answers as [[...];[...];...]

Answer: ((p2||p2)=(p4&p1))

Answer: (~p4=(p2=>p3))

Answer: ((p4=>p2)||(p1&p4))


Prompt:
Given:
p1: 2 is considered lucky.
p2: 5 is odd.
p3: 7 is a prime number.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that 2 is considered lucky. and 7 is a prime number.
(2) p3=>p2 and p1=>p3
(3) It is not the case that It is not the case that 7 is a prime number.
(4) It is not the case that 2 is considered lucky. and It is not the case that 7 is a prime number.

Format your answers as [[...];[...];...]

Answer: ~(p1&p3)

Answer: ((p3=>p2)&(p1=>p3))

Answer: ~~p3

Answer: (~p1&~p3)


Prompt:
Given:
p1: Pi is divisible by 3.
p2: Red is odd.
p3: Blue is odd.
p4: Square root of 3 is considered lucky.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that Square root of 3 is considered lucky. and Red is odd.
(2) Blue is odd. and p2=p2=>p2
(3) p2=p2=p1=p3

Format your answers as [[...];[...];...]

Answer: ~(p4&p2)

Answer: ((p3&p2)=(p2=>p2))

Answer: ((p2=p2)=(p1=p3))


Prompt:
Given:
p1: Pi is even.
p2: Square root of 3 is a fruit.
p3: 4 is a common color.
p4: Red is a common color.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that 4 is a common color. and p2=p1
(2) It is not the case that p2=p3 and 4 is a common color.
(3) p2=>p1 and p3=>p4

Format your answers as [[...];[...];...]

Answer: (~p3&(p2=p1))

Answer: (~p2=(p3&p3))

Answer: ((p2=>p1)&(p3=>p4))


Prompt:
Given:
p1: 4 is divisible by 3.
p2: 5 is divisible by 3.
p3: Blue is odd.

Symbolize the following propositions using &, ||, ~:
(1) Blue is odd. and p1=>p2 and 5 is divisible by 3.
(2) It is not the case that It is not the case that 5 is divisible by 3.
(3) It is not the case that p2=>p1 and 4 is divisible by 3.
(4) p3=>p2=>p3=>p1

Format your answers as [[...];[...];...]

Answer: ((p3&p1)=>(p2&p2))

Answer: ~~p2

Answer: (~p2=>(p1&p1))

Answer: ((p3=>p2)=>(p3=>p1))


Prompt:
Given:
p1: 7 is a prime number.
p2: 5 is a prime number.
p3: Blue is odd.

Symbolize the following propositions using &, ||, ~:
(1) 7 is a prime number. and p2=> It is not the case that 7 is a prime number.
(2) It is not the case that p2=>p1 and 7 is a prime number.
(3) It is not the case that p2=>p2
(4) It is not the case that Blue is odd. and p3=>p3

Format your answers as [[...];[...];...]

Answer: ((p1&p2)=>~p1)

Answer: (~p2=>(p1&p1))

Answer: ~(p2=>p2)

Answer: (~p3&(p3=>p3))


Prompt:
Given:
p1: Blue is a prime number.
p2: 5 is odd.
p3: Pi is a common color.

Symbolize the following propositions using &, ||, ~:
(1) Blue is a prime number. and Pi is a common color. and It is not the case that Pi is a common color.
(2) It is not the case that 5 is odd. or It is not the case that Blue is a prime number.
(3) It is not the case that It is not the case that 5 is odd.

Format your answers as [[...];[...];...]

Answer: ((p1&p3)&~p3)

Answer: (~p2||~p1)

Answer: ~~p2


Prompt:
Given:
p1: 4 is considered lucky.
p2: 2 is a fruit.

Symbolize the following propositions using &, ||, ~:
(1) 2 is a fruit. or 2 is a fruit. and It is not the case that 4 is considered lucky.
(2) 4 is considered lucky. and 2 is a fruit. or It is not the case that 2 is a fruit.
(3) It is not the case that 2 is a fruit. and 2 is a fruit. and 4 is considered lucky.
(4) 2 is a fruit. or 4 is considered lucky. or 4 is considered lucky. or 4 is considered lucky.
(5) It is not the case that 2 is a fruit. or 2 is a fruit. and 4 is considered lucky.

Format your answers as [[...];[...];...]

Answer: ((p2||p2)&~p1)

Answer: ((p1&p2)||~p2)

Answer: (~p2&(p2&p1))

Answer: ((p2||p1)||(p1||p1))

Answer: (~p2||(p2&p1))


Prompt:
Given:
p1: 2 is a common color.
p2: 4 is odd.

Symbolize the following propositions using &, ||, ~:
(1) 2 is a common color. and 2 is a common color. or 2 is a common color. or 2 is a common color.
(2) 2 is a common color. and 4 is odd. and It is not the case that 4 is odd.
(3) It is not the case that It is not the case that 2 is a common color.
(4) It is not the case that 4 is odd. or 2 is a common color.
(5) It is not the case that 2 is a common color. or 4 is odd.

Format your answers as [[...];[...];...]

Answer: ((p1&p1)||(p1||p1))

Answer: ((p1&p2)&~p2)

Answer: ~~p1

Answer: ~(p2||p1)

Answer: ~(p1||p2)


Prompt:
Given:
p1: 7 is a common color.
p2: 2 is a common color.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that 7 is a common color. or 2 is a common color.
(2) It is not the case that 7 is a common color. and 7 is a common color. and 7 is a common color.
(3) 2 is a common color. and 2 is a common color. and It is not the case that 7 is a common color.
(4) It is not the case that 7 is a common color. or 2 is a common color.
(5) It is not the case that 7 is a common color. or It is not the case that 7 is a common color.

Format your answers as [[...];[...];...]

Answer: ~(p1||p2)

Answer: (~p1&(p1&p1))

Answer: ((p2&p2)&~p1)

Answer: ~(p1||p2)

Answer: (~p1||~p1)


Prompt:
Given:
p1: Square root of 3 is a prime number.
p2: Pi is odd.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that Pi is odd. and Square root of 3 is a prime number. and Square root of 3 is a prime number.
(2) It is not the case that Square root of 3 is a prime number. or Square root of 3 is a prime number. or Square root of 3 is a prime number.
(3) Pi is odd. and Square root of 3 is a prime number. and Square root of 3 is a prime number. or Square root of 3 is a prime number.
(4) It is not the case that Pi is odd. and Square root of 3 is a prime number. or Pi is odd.
(5) Pi is odd. or Square root of 3 is a prime number. or Pi is odd. and Pi is odd.

Format your answers as [[...];[...];...]

Answer: (~p2&(p1&p1))

Answer: (~p1||(p1||p1))

Answer: ((p2&p1)&(p1||p1))

Answer: (~p2&(p1||p2))

Answer: ((p2||p1)||(p2&p2))


Prompt:
Given:
p1: Pi is a prime number.
p2: Red is odd.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that It is not the case that Pi is a prime number.
(2) It is not the case that Red is odd. and Pi is a prime number. and Pi is a prime number.
(3) Red is odd. and Red is odd. and Red is odd. and Pi is a prime number.
(4) It is not the case that It is not the case that Red is odd.
(5) It is not the case that Pi is a prime number. and Red is odd.

Format your answers as [[...];[...];...]

Answer: ~~p1

Answer: (~p2&(p1&p1))

Answer: ((p2&p2)&(p2&p1))

Answer: ~~p2

Answer: ~(p1&p2)


Prompt:
Given:
p1: 5 is a fruit.
p2: Square root of 3 is a prime number.
p3: 2 is a prime number.

Symbolize the following propositions using &, ||, ~:
(1) 2 is a prime number. or 5 is a fruit. or 5 is a fruit. and 5 is a fruit.
(2) 2 is a prime number. and 2 is a prime number. and It is not the case that Square root of 3 is a prime number.
(3) 5 is a fruit. or 2 is a prime number. or 2 is a prime number. and 2 is a prime number.

Format your answers as [[...];[...];...]

Answer: ((p3||p1)||(p1&p1))

Answer: ((p3&p3)&~p2)

Answer: ((p1||p3)||(p3&p3))


Prompt:
Given:
p1: Red is a prime number.
p2: 5 is even.
p3: 4 is a prime number.
p4: Pi is divisible by 3.

Symbolize the following propositions using &, ||, ~:
(1) Red is a prime number. or 4 is a prime number. and It is not the case that Pi is divisible by 3.
(2) 5 is even. or p2=p1=>p2
(3) p4=p1 and It is not the case that 4 is a prime number.

Format your answers as [[...];[...];...]

Answer: ((p1||p3)&~p4)

Answer: ((p2||p2)=(p1=>p2))

Answer: ((p4=p1)&~p3)


Prompt:
Given:
p1: Blue is odd.
p2: 7 is divisible by 3.
p3: Red is a common color.
p4: 4 is odd.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that p2= It is not the case that Blue is odd.
(2) 4 is odd. or 4 is odd. or It is not the case that 4 is odd.
(3) Blue is odd. and Red is a common color. or It is not the case that 4 is odd.

Format your answers as [[...];[...];...]

Answer: (~p2=~p1)

Answer: ((p4||p4)||~p4)

Answer: ((p1&p3)||~p4)


Prompt:
Given:
p1: 2 is considered lucky.
p2: Square root of 3 is divisible by 3.

Symbolize the following propositions using &, ||, ~:
(1) 2 is considered lucky. or 2 is considered lucky. or Square root of 3 is divisible by 3. or 2 is considered lucky.
(2) It is not the case that 2 is considered lucky. or 2 is considered lucky.
(3) Square root of 3 is divisible by 3. or Square root of 3 is divisible by 3. and 2 is considered lucky. and Square root of 3 is divisible by 3.
(4) It is not the case that 2 is considered lucky. and Square root of 3 is divisible by 3.
(5) It is not the case that Square root of 3 is divisible by 3. and 2 is considered lucky.

Format your answers as [[...];[...];...]

Answer: ((p1||p1)||(p2||p1))

Answer: ~(p1||p1)

Answer: ((p2||p2)&(p1&p2))

Answer: ~(p1&p2)

Answer: ~(p2&p1)


Prompt:
Given:
p1: Red is divisible by 3.
p2: Blue is a common color.
p3: Pi is odd.

Symbolize the following propositions using &, ||, ~:
(1) p2=>p3=> It is not the case that Red is divisible by 3.
(2) It is not the case that It is not the case that Blue is a common color.
(3) Pi is odd. and p3=>p3 and Red is divisible by 3.
(4) Blue is a common color. and Red is divisible by 3. and p1=>p3

Format your answers as [[...];[...];...]

Answer: ((p2=>p3)=>~p1)

Answer: ~~p2

Answer: ((p3&p3)=>(p3&p1))

Answer: ((p2&p1)&(p1=>p3))


Prompt:
Given:
p1: Blue is even.
p2: 4 is odd.
p3: 5 is a fruit.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that 5 is a fruit. and 5 is a fruit. and Blue is even.
(2) It is not the case that 4 is odd. and 5 is a fruit. and 4 is odd.
(3) It is not the case that It is not the case that 5 is a fruit.

Format your answers as [[...];[...];...]

Answer: (~p3&(p3&p1))

Answer: (~p2&(p3&p2))

Answer: ~~p3


Prompt:
Given:
p1: Blue is divisible by 3.
p2: 7 is considered lucky.
p3: 2 is odd.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that 7 is considered lucky. and 2 is odd. and 7 is considered lucky.
(2) It is not the case that Blue is divisible by 3. and Blue is divisible by 3.
(3) Blue is divisible by 3. and 7 is considered lucky. or 2 is odd. and 2 is odd.

Format your answers as [[...];[...];...]

Answer: (~p2&(p3&p2))

Answer: ~(p1&p1)

Answer: ((p1&p2)||(p3&p3))


Prompt:
Given:
p1: 7 is odd.
p2: 2 is a fruit.
p3: Blue is a prime number.

Symbolize the following propositions using &, ||, ~:
(1) p1=>p3 and It is not the case that Blue is a prime number.
(2) p3=>p3=>p2=>p2
(3) 2 is a fruit. and 2 is a fruit. and 2 is a fruit. and 2 is a fruit.
(4) Blue is a prime number. and Blue is a prime number. and p1=>p1

Format your answers as [[...];[...];...]

Answer: ((p1=>p3)&~p3)

Answer: ((p3=>p3)=>(p2=>p2))

Answer: ((p2&p2)&(p2&p2))

Answer: ((p3&p3)&(p1=>p1))


Prompt:
Given:
p1: 4 is a common color.
p2: Pi is a prime number.
p3: Blue is a prime number.

Symbolize the following propositions using &, ||, ~:
(1) p2=>p3=>p3=>p3
(2) p2=>p1=>p1 and Pi is a prime number.
(3) It is not the case that It is not the case that Blue is a prime number.
(4) It is not the case that p3=>p2

Format your answers as [[...];[...];...]

Answer: ((p2=>p3)=>(p3=>p3))

Answer: ((p2=>p1)=>(p1&p2))

Answer: ~~p3

Answer: ~(p3=>p2)


Prompt:
Given:
p1: 4 is a fruit.
p2: Red is a common color.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that 4 is a fruit. and Red is a common color.
(2) Red is a common color. and 4 is a fruit. and Red is a common color. or Red is a common color.
(3) Red is a common color. or Red is a common color. and 4 is a fruit. or Red is a common color.
(4) Red is a common color. and Red is a common color. or It is not the case that 4 is a fruit.
(5) 4 is a fruit. and Red is a common color. and It is not the case that 4 is a fruit.

Format your answers as [[...];[...];...]

Answer: ~(p1&p2)

Answer: ((p2&p1)&(p2||p2))

Answer: ((p2||p2)&(p1||p2))

Answer: ((p2&p2)||~p1)

Answer: ((p1&p2)&~p1)


Prompt:
Given:
p1: 7 is a common color.
p2: 2 is even.
p3: 4 is a common color.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that 7 is a common color. and 4 is a common color.
(2) It is not the case that 4 is a common color. and 2 is even.
(3) It is not the case that 2 is even. and 2 is even. or 4 is a common color.

Format your answers as [[...];[...];...]

Answer: ~(p1&p3)

Answer: ~(p3&p2)

Answer: (~p2&(p2||p3))


Prompt:
Given:
p1: 4 is a fruit.
p2: 7 is considered lucky.
p3: 5 is a fruit.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that 4 is a fruit. or 4 is a fruit. or 7 is considered lucky.
(2) 4 is a fruit. and 7 is considered lucky. or It is not the case that 4 is a fruit.
(3) It is not the case that It is not the case that 4 is a fruit.

Format your answers as [[...];[...];...]

Answer: (~p1||(p1||p2))

Answer: ((p1&p2)||~p1)

Answer: ~~p1


Prompt:
Given:
p1: 5 is odd.
p2: 7 is even.
p3: Blue is even.
p4: 2 is considered lucky.

Symbolize the following propositions using &, ||, ~:
(1) p1=p1 or Blue is even. or Blue is even.
(2) p4=>p1=>p1 or 7 is even.
(3) 7 is even. or 5 is odd. or It is not the case that 5 is odd.

Format your answers as [[...];[...];...]

Answer: ((p1=p1)||(p3||p3))

Answer: ((p4=>p1)=>(p1||p2))

Answer: ((p2||p1)||~p1)


Prompt:
Given:
p1: 5 is odd.
p2: 7 is a common color.
p3: Pi is odd.

Symbolize the following propositions using &, ||, ~:
(1) Pi is odd. or 5 is odd. or It is not the case that Pi is odd.
(2) It is not the case that It is not the case that Pi is odd.
(3) Pi is odd. and Pi is odd. and 7 is a common color. and 5 is odd.

Format your answers as [[...];[...];...]

Answer: ((p3||p1)||~p3)

Answer: ~~p3

Answer: ((p3&p3)&(p2&p1))


Prompt:
Given:
p1: 7 is a fruit.
p2: Blue is odd.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that It is not the case that Blue is odd.
(2) It is not the case that It is not the case that Blue is odd.
(3) Blue is odd. and 7 is a fruit. or Blue is odd. or 7 is a fruit.
(4) 7 is a fruit. and Blue is odd. and Blue is odd. and 7 is a fruit.
(5) It is not the case that 7 is a fruit. and It is not the case that 7 is a fruit.

Format your answers as [[...];[...];...]

Answer: ~~p2

Answer: ~~p2

Answer: ((p2&p1)||(p2||p1))

Answer: ((p1&p2)&(p2&p1))

Answer: (~p1&~p1)


Prompt:
Given:
p1: 7 is even.
p2: 5 is considered lucky.
p3: Square root of 3 is odd.

Symbolize the following propositions using &, ||, ~:
(1) 7 is even. or 5 is considered lucky. or Square root of 3 is odd. and 5 is considered lucky.
(2) 7 is even. or 7 is even. or It is not the case that 5 is considered lucky.
(3) It is not the case that Square root of 3 is odd. or 5 is considered lucky. or 5 is considered lucky.

Format your answers as [[...];[...];...]

Answer: ((p1||p2)||(p3&p2))

Answer: ((p1||p1)||~p2)

Answer: (~p3||(p2||p2))


Prompt:
Given:
p1: Pi is a common color.
p2: 5 is odd.
p3: Blue is divisible by 3.

Symbolize the following propositions using &, ||, ~:
(1) Blue is divisible by 3. and Blue is divisible by 3. and 5 is odd. and Blue is divisible by 3.
(2) It is not the case that p3=>p2
(3) It is not the case that Blue is divisible by 3. and Pi is a common color.
(4) p1=>p2 and p3=>p1

Format your answers as [[...];[...];...]

Answer: ((p3&p3)&(p2&p3))

Answer: ~(p3=>p2)

Answer: ~(p3&p1)

Answer: ((p1=>p2)&(p3=>p1))


Prompt:
Given:
p1: Red is divisible by 3.
p2: Pi is even.
p3: Blue is a prime number.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that Pi is even. and Pi is even.
(2) It is not the case that It is not the case that Red is divisible by 3.
(3) It is not the case that p3=>p2
(4) p3=>p3=>p3 and Blue is a prime number.

Format your answers as [[...];[...];...]

Answer: ~(p2&p2)

Answer: ~~p1

Answer: ~(p3=>p2)

Answer: ((p3=>p3)=>(p3&p3))


Prompt:
Given:
p1: 5 is odd.
p2: 7 is odd.
p3: Blue is a fruit.
p4: Square root of 3 is even.

Symbolize the following propositions using &, ||, ~:
(1) Blue is a fruit. and p1=> It is not the case that 5 is odd.
(2) It is not the case that 5 is odd. and Square root of 3 is even.
(3) p1=>p2=p1 and 5 is odd.

Format your answers as [[...];[...];...]

Answer: ((p3&p1)=>~p1)

Answer: ~(p1&p4)

Answer: ((p1=>p2)=(p1&p1))


Prompt:
Given:
p1: Red is divisible by 3.
p2: 4 is even.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that It is not the case that Red is divisible by 3.
(2) Red is divisible by 3. or Red is divisible by 3. or Red is divisible by 3. or 4 is even.
(3) 4 is even. and 4 is even. and Red is divisible by 3. or Red is divisible by 3.
(4) 4 is even. or Red is divisible by 3. and It is not the case that 4 is even.
(5) It is not the case that Red is divisible by 3. and It is not the case that Red is divisible by 3.

Format your answers as [[...];[...];...]

Answer: ~~p1

Answer: ((p1||p1)||(p1||p2))

Answer: ((p2&p2)&(p1||p1))

Answer: ((p2||p1)&~p2)

Answer: (~p1&~p1)


Prompt:
Given:
p1: Square root of 3 is even.
p2: 2 is a prime number.
p3: Pi is a common color.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that 2 is a prime number. and It is not the case that 2 is a prime number.
(2) Pi is a common color. and Pi is a common color. and Square root of 3 is even. and 2 is a prime number.
(3) Pi is a common color. or Square root of 3 is even. or 2 is a prime number. or Square root of 3 is even.

Format your answers as [[...];[...];...]

Answer: (~p2&~p2)

Answer: ((p3&p3)&(p1&p2))

Answer: ((p3||p1)||(p2||p1))


Prompt:
Given:
p1: 7 is divisible by 3.
p2: Blue is even.
p3: Red is even.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that 7 is divisible by 3. and Blue is even.
(2) It is not the case that It is not the case that Blue is even.
(3) It is not the case that Blue is even. and 7 is divisible by 3. and 7 is divisible by 3.
(4) It is not the case that It is not the case that Blue is even.

Format your answers as [[...];[...];...]

Answer: ~(p1&p2)

Answer: ~~p2

Answer: (~p2&(p1&p1))

Answer: ~~p2


Prompt:
Given:
p1: 4 is odd.
p2: 7 is a prime number.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that 4 is odd. or 7 is a prime number.
(2) It is not the case that 4 is odd. and 4 is odd. or 7 is a prime number.
(3) It is not the case that It is not the case that 4 is odd.
(4) It is not the case that It is not the case that 4 is odd.
(5) 4 is odd. and 7 is a prime number. or 4 is odd. or 7 is a prime number.

Format your answers as [[...];[...];...]

Answer: ~(p1||p2)

Answer: (~p1&(p1||p2))

Answer: ~~p1

Answer: ~~p1

Answer: ((p1&p2)||(p1||p2))


Prompt:
Given:
p1: Square root of 3 is odd.
p2: Pi is a prime number.

Symbolize the following propositions using &, ||, ~:
(1) Pi is a prime number. and Square root of 3 is odd. or Square root of 3 is odd. and Square root of 3 is odd.
(2) Square root of 3 is odd. and Square root of 3 is odd. and It is not the case that Square root of 3 is odd.
(3) Pi is a prime number. and Square root of 3 is odd. or Square root of 3 is odd. or Pi is a prime number.
(4) It is not the case that It is not the case that Square root of 3 is odd.
(5) Pi is a prime number. or Square root of 3 is odd. and It is not the case that Pi is a prime number.

Format your answers as [[...];[...];...]

Answer: ((p2&p1)||(p1&p1))

Answer: ((p1&p1)&~p1)

Answer: ((p2&p1)||(p1||p2))

Answer: ~~p1

Answer: ((p2||p1)&~p2)


Prompt:
Given:
p1: Square root of 3 is odd.
p2: 7 is even.
p3: Red is a prime number.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that Red is a prime number. or 7 is even.
(2) It is not the case that Square root of 3 is odd. and Square root of 3 is odd. or Square root of 3 is odd.
(3) It is not the case that 7 is even. or 7 is even.

Format your answers as [[...];[...];...]

Answer: ~(p3||p2)

Answer: (~p1&(p1||p1))

Answer: ~(p2||p2)


Prompt:
Given:
p1: 5 is considered lucky.
p2: Square root of 3 is even.
p3: 2 is odd.
p4: 4 is odd.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that 4 is odd. and Square root of 3 is even.
(2) p1=>p1=>p2 and 5 is considered lucky.
(3) 2 is odd. or p2=>p4=p3

Format your answers as [[...];[...];...]

Answer: ~(p4&p2)

Answer: ((p1=>p1)=>(p2&p1))

Answer: ((p3||p2)=>(p4=p3))


Prompt:
Given:
p1: Red is divisible by 3.
p2: Pi is a prime number.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that Pi is a prime number. and It is not the case that Pi is a prime number.
(2) Red is divisible by 3. or Red is divisible by 3. and It is not the case that Red is divisible by 3.
(3) It is not the case that It is not the case that Pi is a prime number.
(4) It is not the case that It is not the case that Pi is a prime number.
(5) It is not the case that Red is divisible by 3. or Pi is a prime number.

Format your answers as [[...];[...];...]

Answer: (~p2&~p2)

Answer: ((p1||p1)&~p1)

Answer: ~~p2

Answer: ~~p2

Answer: ~(p1||p2)


Prompt:
Given:
p1: Square root of 3 is even.
p2: Blue is even.
p3: 4 is a common color.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that Square root of 3 is even. and p1=>p3
(2) p1=>p2=> It is not the case that Square root of 3 is even.
(3) p3=>p3 and 4 is a common color. and Square root of 3 is even.
(4) It is not the case that It is not the case that Square root of 3 is even.

Format your answers as [[...];[...];...]

Answer: (~p1&(p1=>p3))

Answer: ((p1=>p2)=>~p1)

Answer: ((p3=>p3)&(p3&p1))

Answer: ~~p1


Prompt:
Given:
p1: 7 is odd.
p2: Blue is a fruit.
p3: 4 is a common color.

Symbolize the following propositions using &, ||, ~:
(1) Blue is a fruit. and Blue is a fruit. or 7 is odd. and 4 is a common color.
(2) 7 is odd. or Blue is a fruit. and 7 is odd. and Blue is a fruit.
(3) It is not the case that 4 is a common color. or Blue is a fruit.

Format your answers as [[...];[...];...]

Answer: ((p2&p2)||(p1&p3))

Answer: ((p1||p2)&(p1&p2))

Answer: ~(p3||p2)


Prompt:
Given:
p1: 2 is a fruit.
p2: 5 is odd.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that 5 is odd. and 5 is odd.
(2) It is not the case that 5 is odd. or 5 is odd. and 5 is odd.
(3) It is not the case that 2 is a fruit. and 5 is odd.
(4) 2 is a fruit. or 5 is odd. or 5 is odd. or 5 is odd.
(5) 2 is a fruit. and 2 is a fruit. or It is not the case that 2 is a fruit.

Format your answers as [[...];[...];...]

Answer: ~(p2&p2)

Answer: (~p2||(p2&p2))

Answer: ~(p1&p2)

Answer: ((p1||p2)||(p2||p2))

Answer: ((p1&p1)||~p1)


Prompt:
Given:
p1: 2 is a prime number.
p2: Blue is a fruit.
p3: 4 is considered lucky.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that 2 is a prime number. and 2 is a prime number. or 2 is a prime number.
(2) It is not the case that Blue is a fruit. or 2 is a prime number. and 2 is a prime number.
(3) 4 is considered lucky. or 4 is considered lucky. or It is not the case that 4 is considered lucky.

Format your answers as [[...];[...];...]

Answer: (~p1&(p1||p1))

Answer: (~p2||(p1&p1))

Answer: ((p3||p3)||~p3)


Prompt:
Given:
p1: Red is divisible by 3.
p2: Square root of 3 is divisible by 3.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that Square root of 3 is divisible by 3. and Square root of 3 is divisible by 3. and Square root of 3 is divisible by 3.
(2) It is not the case that Red is divisible by 3. and Red is divisible by 3. and Square root of 3 is divisible by 3.
(3) It is not the case that Square root of 3 is divisible by 3. or Red is divisible by 3.
(4) Square root of 3 is divisible by 3. or Red is divisible by 3. and It is not the case that Square root of 3 is divisible by 3.
(5) It is not the case that Red is divisible by 3. and Square root of 3 is divisible by 3. and Red is divisible by 3.

Format your answers as [[...];[...];...]

Answer: (~p2&(p2&p2))

Answer: (~p1&(p1&p2))

Answer: ~(p2||p1)

Answer: ((p2||p1)&~p2)

Answer: (~p1&(p2&p1))


Prompt:
Given:
p1: Red is divisible by 3.
p2: Pi is divisible by 3.
p3: 7 is divisible by 3.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that p1=>p2
(2) p2=>p1 and Red is divisible by 3. and Red is divisible by 3.
(3) p2=>p2=>p2 and Pi is divisible by 3.
(4) Red is divisible by 3. and p1=>p2=>p3

Format your answers as [[...];[...];...]

Answer: ~(p1=>p2)

Answer: ((p2=>p1)&(p1&p1))

Answer: ((p2=>p2)=>(p2&p2))

Answer: ((p1&p1)=>(p2=>p3))


Prompt:
Given:
p1: 4 is a prime number.
p2: Pi is a fruit.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that Pi is a fruit. or 4 is a prime number. or 4 is a prime number.
(2) Pi is a fruit. or 4 is a prime number. and Pi is a fruit. or Pi is a fruit.
(3) 4 is a prime number. or 4 is a prime number. and It is not the case that 4 is a prime number.
(4) Pi is a fruit. and 4 is a prime number. or Pi is a fruit. and Pi is a fruit.
(5) 4 is a prime number. and Pi is a fruit. or 4 is a prime number. or Pi is a fruit.

Format your answers as [[...];[...];...]

Answer: (~p2||(p1||p1))

Answer: ((p2||p1)&(p2||p2))

Answer: ((p1||p1)&~p1)

Answer: ((p2&p1)||(p2&p2))

Answer: ((p1&p2)||(p1||p2))


Prompt:
Given:
p1: 7 is a fruit.
p2: Red is odd.
p3: Blue is a common color.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that It is not the case that Red is odd.
(2) It is not the case that It is not the case that Blue is a common color.
(3) Red is odd. and p1=>p3=>p2
(4) It is not the case that Red is odd. and Red is odd.

Format your answers as [[...];[...];...]

Answer: ~~p2

Answer: ~~p3

Answer: ((p2&p1)=>(p3=>p2))

Answer: ~(p2&p2)


Prompt:
Given:
p1: 4 is a fruit.
p2: 2 is even.
p3: 5 is a fruit.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that It is not the case that 2 is even.
(2) p3=>p3=>p2=>p3
(3) It is not the case that 5 is a fruit. and 2 is even.
(4) It is not the case that 2 is even. and p2=>p1

Format your answers as [[...];[...];...]

Answer: ~~p2

Answer: ((p3=>p3)=>(p2=>p3))

Answer: ~(p3&p2)

Answer: (~p2&(p2=>p1))


Prompt:
Given:
p1: 7 is a prime number.
p2: 4 is a fruit.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that 4 is a fruit. or 7 is a prime number. or 4 is a fruit.
(2) It is not the case that 7 is a prime number. and It is not the case that 7 is a prime number.
(3) 7 is a prime number. and 4 is a fruit. and It is not the case that 7 is a prime number.
(4) It is not the case that 4 is a fruit. and 7 is a prime number.
(5) It is not the case that It is not the case that 4 is a fruit.

Format your answers as [[...];[...];...]

Answer: (~p2||(p1||p2))

Answer: (~p1&~p1)

Answer: ((p1&p2)&~p1)

Answer: ~(p2&p1)

Answer: ~~p2


Prompt:
Given:
p1: Blue is considered lucky.
p2: Red is a prime number.
p3: 7 is a fruit.
p4: 2 is a prime number.

Symbolize the following propositions using &, ||, ~:
(1) p1=p1 or 2 is a prime number. or 7 is a fruit.
(2) 2 is a prime number. or 7 is a fruit. or Blue is considered lucky. and Blue is considered lucky.
(3) It is not the case that 7 is a fruit. and Blue is considered lucky.

Format your answers as [[...];[...];...]

Answer: ((p1=p1)||(p4||p3))

Answer: ((p4||p3)||(p1&p1))

Answer: ~(p3&p1)


Prompt:
Given:
p1: Pi is odd.
p2: Square root of 3 is divisible by 3.

Symbolize the following propositions using &, ||, ~:
(1) Square root of 3 is divisible by 3. or Pi is odd. and It is not the case that Pi is odd.
(2) It is not the case that It is not the case that Square root of 3 is divisible by 3.
(3) It is not the case that Square root of 3 is divisible by 3. or Pi is odd.
(4) It is not the case that Pi is odd. and Pi is odd.
(5) Pi is odd. or Pi is odd. or Pi is odd. and Pi is odd.

Format your answers as [[...];[...];...]

Answer: ((p2||p1)&~p1)

Answer: ~~p2

Answer: ~(p2||p1)

Answer: ~(p1&p1)

Answer: ((p1||p1)||(p1&p1))


Prompt:
Given:
p1: 5 is divisible by 3.
p2: 4 is considered lucky.
p3: Blue is a common color.
p4: Pi is a common color.

Symbolize the following propositions using &, ||, ~:
(1) Blue is a common color. or p3=p1 or 5 is divisible by 3.
(2) 5 is divisible by 3. and p1=>p4=>p1
(3) p4=p4=>p1=>p4

Format your answers as [[...];[...];...]

Answer: ((p3||p3)=(p1||p1))

Answer: ((p1&p1)=>(p4=>p1))

Answer: ((p4=p4)=>(p1=>p4))


Prompt:
Given:
p1: 5 is divisible by 3.
p2: 4 is odd.
p3: 2 is divisible by 3.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that 4 is odd. and 4 is odd.
(2) 2 is divisible by 3. or 4 is odd. and It is not the case that 4 is odd.
(3) It is not the case that 2 is divisible by 3. and 5 is divisible by 3. and 5 is divisible by 3.

Format your answers as [[...];[...];...]

Answer: ~(p2&p2)

Answer: ((p3||p2)&~p2)

Answer: (~p3&(p1&p1))


Prompt:
Given:
p1: 7 is a prime number.
p2: 4 is a common color.

Symbolize the following propositions using &, ||, ~:
(1) 4 is a common color. or 4 is a common color. and It is not the case that 4 is a common color.
(2) It is not the case that 4 is a common color. or 4 is a common color. and 4 is a common color.
(3) It is not the case that 4 is a common color. and 7 is a prime number.
(4) It is not the case that 7 is a prime number. or 7 is a prime number. and 4 is a common color.
(5) It is not the case that 4 is a common color. or It is not the case that 7 is a prime number.

Format your answers as [[...];[...];...]

Answer: ((p2||p2)&~p2)

Answer: (~p2||(p2&p2))

Answer: ~(p2&p1)

Answer: (~p1||(p1&p2))

Answer: (~p2||~p1)


Prompt:
Given:
p1: 5 is odd.
p2: 7 is a common color.
p3: Blue is even.

Symbolize the following propositions using &, ||, ~:
(1) Blue is even. and 7 is a common color. or Blue is even. and Blue is even.
(2) It is not the case that Blue is even. or It is not the case that 7 is a common color.
(3) It is not the case that It is not the case that 5 is odd.

Format your answers as [[...];[...];...]

Answer: ((p3&p2)||(p3&p3))

Answer: (~p3||~p2)

Answer: ~~p1


Prompt:
Given:
p1: Square root of 3 is odd.
p2: 5 is odd.

Symbolize the following propositions using &, ||, ~:
(1) Square root of 3 is odd. and 5 is odd. and 5 is odd. or 5 is odd.
(2) It is not the case that Square root of 3 is odd. or Square root of 3 is odd.
(3) Square root of 3 is odd. or Square root of 3 is odd. or Square root of 3 is odd. and Square root of 3 is odd.
(4) It is not the case that It is not the case that 5 is odd.
(5) It is not the case that Square root of 3 is odd. and 5 is odd. and 5 is odd.

Format your answers as [[...];[...];...]

Answer: ((p1&p2)&(p2||p2))

Answer: ~(p1||p1)

Answer: ((p1||p1)||(p1&p1))

Answer: ~~p2

Answer: (~p1&(p2&p2))


Prompt:
Given:
p1: 5 is even.
p2: 2 is even.
p3: Blue is a prime number.

Symbolize the following propositions using &, ||, ~:
(1) Blue is a prime number. and Blue is a prime number. and 5 is even. and 5 is even.
(2) It is not the case that p1=>p2
(3) It is not the case that It is not the case that 2 is even.
(4) It is not the case that Blue is a prime number. and Blue is a prime number. and Blue is a prime number.

Format your answers as [[...];[...];...]

Answer: ((p3&p3)&(p1&p1))

Answer: ~(p1=>p2)

Answer: ~~p2

Answer: (~p3&(p3&p3))


Prompt:
Given:
p1: Pi is odd.
p2: Red is a prime number.
p3: Blue is even.

Symbolize the following propositions using &, ||, ~:
(1) Pi is odd. and p3=> It is not the case that Pi is odd.
(2) It is not the case that It is not the case that Blue is even.
(3) It is not the case that Red is a prime number. and Blue is even.
(4) p1=>p1=>p3 and Red is a prime number.

Format your answers as [[...];[...];...]

Answer: ((p1&p3)=>~p1)

Answer: ~~p3

Answer: ~(p2&p3)

Answer: ((p1=>p1)=>(p3&p2))


Prompt:
Given:
p1: 7 is a prime number.
p2: Red is even.
p3: 4 is a prime number.
p4: 5 is odd.

Symbolize the following propositions using &, ||, ~:
(1) 5 is odd. and p1=> It is not the case that Red is even.
(2) It is not the case that p1=>p1
(3) p2=>p3=>p2=>p1

Format your answers as [[...];[...];...]

Answer: ((p4&p1)=>~p2)

Answer: ~(p1=>p1)

Answer: ((p2=>p3)=>(p2=>p1))


Prompt:
Given:
p1: Square root of 3 is a prime number.
p2: 2 is odd.
p3: Pi is even.
p4: 7 is odd.

Symbolize the following propositions using &, ||, ~:
(1) p3=p3 and p4=p1
(2) p1=>p3 or It is not the case that Pi is even.
(3) It is not the case that p2=p4

Format your answers as [[...];[...];...]

Answer: ((p3=p3)&(p4=p1))

Answer: ((p1=>p3)||~p3)

Answer: ~(p2=p4)


Prompt:
Given:
p1: 7 is divisible by 3.
p2: Blue is considered lucky.
p3: 4 is a fruit.
p4: Red is divisible by 3.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that 7 is divisible by 3. and Red is divisible by 3.
(2) 4 is a fruit. and Blue is considered lucky. or It is not the case that Red is divisible by 3.
(3) It is not the case that 7 is divisible by 3. and 4 is a fruit.

Format your answers as [[...];[...];...]

Answer: ~(p1&p4)

Answer: ((p3&p2)||~p4)

Answer: ~(p1&p3)


Prompt:
Given:
p1: Red is a prime number.
p2: Pi is a common color.
p3: Square root of 3 is considered lucky.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that p2=>p3
(2) It is not the case that p3=>p3 and Square root of 3 is considered lucky.
(3) It is not the case that p2=>p2=>p2
(4) Pi is a common color. and p3=>p2=>p3

Format your answers as [[...];[...];...]

Answer: ~(p2=>p3)

Answer: (~p3=>(p3&p3))

Answer: (~p2=>(p2=>p2))

Answer: ((p2&p3)=>(p2=>p3))


Prompt:
Given:
p1: 2 is divisible by 3.
p2: Square root of 3 is divisible by 3.
p3: 4 is a common color.
p4: Red is even.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that It is not the case that 2 is divisible by 3.
(2) p1=p2=p2=>p4
(3) Red is even. and 2 is divisible by 3. and p1=>p1

Format your answers as [[...];[...];...]

Answer: ~~p1

Answer: ((p1=p2)=(p2=>p4))

Answer: ((p4&p1)&(p1=>p1))


Prompt:
Given:
p1: 5 is a common color.
p2: Pi is a common color.
p3: 4 is odd.

Symbolize the following propositions using &, ||, ~:
(1) Pi is a common color. and Pi is a common color. and p2=>p2
(2) p1=>p2 and p1=>p2
(3) 5 is a common color. and p1=>p2 and Pi is a common color.
(4) 5 is a common color. and Pi is a common color. and 4 is odd. and Pi is a common color.

Format your answers as [[...];[...];...]

Answer: ((p2&p2)&(p2=>p2))

Answer: ((p1=>p2)&(p1=>p2))

Answer: ((p1&p1)=>(p2&p2))

Answer: ((p1&p2)&(p3&p2))


Prompt:
Given:
p1: Pi is considered lucky.
p2: Blue is odd.

Symbolize the following propositions using &, ||, ~:
(1) Pi is considered lucky. and Blue is odd. and Blue is odd. and Blue is odd.
(2) Blue is odd. and Pi is considered lucky. and Blue is odd. or Blue is odd.
(3) It is not the case that Blue is odd. or Pi is considered lucky.
(4) Blue is odd. or Blue is odd. or Blue is odd. and Blue is odd.
(5) Pi is considered lucky. or Pi is considered lucky. or Blue is odd. and Blue is odd.

Format your answers as [[...];[...];...]

Answer: ((p1&p2)&(p2&p2))

Answer: ((p2&p1)&(p2||p2))

Answer: ~(p2||p1)

Answer: ((p2||p2)||(p2&p2))

Answer: ((p1||p1)||(p2&p2))


Prompt:
Given:
p1: Square root of 3 is a common color.
p2: 5 is odd.
p3: 4 is considered lucky.

Symbolize the following propositions using &, ||, ~:
(1) It is not the case that 5 is odd. or Square root of 3 is a common color.
(2) Square root of 3 is a common color. or 5 is odd. or It is not the case that Square root of 3 is a common color.
(3) 4 is considered lucky. and 4 is considered lucky. and 4 is considered lucky. and 4 is considered lucky.

Format your answers as [[...];[...];...]

Answer: ~(p2||p1)

Answer: ((p1||p2)||~p1)

Answer: ((p3&p3)&(p3&p3))