Question

I don’t understand this and need help! Please help!

Answer 1

$p\implies\sim q$ is true when $p$ is false, or when both $p$ and $\sim q$ are true.

Similarly, $q\implies\sim p$ is true when $q$ is false, or when both $q$ and $\sim p$ are true.

It seems that you are given that $p\implies\sim q$ and $q\implies\sim p$. According to the truth table given above, these can both be true only when one of $p,q$ is true and the other is false.

On the other hand, $p\lor q$ is true when either or both of $p$ or $q$ is true. This is satisfied by the implications in the hypothesis, so $p\lor q$ must be true.