1. Problem: Find the truth value of $q$ if $(\neg p \Rightarrow q) \wedge (\neg q \Leftrightarrow \neg p)$ and $p$ are true. 2. Formula and rules: - $\neg$ means NOT. - $\Rightarrow$ means implication. - $\Leftrightarrow$ means equivalence. - If $p$ is true, then $\neg p$ is false. 3. Step-by-step solution: - Given $p$ is true, so $\neg p$ is false. - Evaluate $\neg p \Rightarrow q$: Since $\neg p$ is false, $\neg p \Rightarrow q$ is true regardless of $q$. - Evaluate $\neg q \Leftrightarrow \neg p$: Since $\neg p$ is false, $\neg q$ must be false for equivalence to hold. - $\neg q$ is false means $q$ is true. 4. Final answer: $q$ is true.