Let p and q represent the following simple statements:

Question

P: I study.

Q: I pass the class.

Write the following compound statement in its symbolic form.

I do not pass the class if and only if I study.

The statement "I do not pass the class if and only if I study." is written ____.

Answer 1

P: I study

Q: I pass the class

I do not pass the class if and only if I study

~Q <--> R

between the ~Q and R is an arrow pointing both left and right. It stands for "if and only if"

it means the same as

(~Q -> P) ^ (P -> ~Q)

the arrow runs both ways

apparently in this scenario studying is very counterproductive.