$(\neg p \Rightarrow p) \wedge (p \Rightarrow \neg q)$
Step-by-Step Solution
Key Concept: Use the equivalence $A \Rightarrow B \equiv \neg A \vee B$ and truth table analysis to determine when compound statements are true.
First, we analyze $(\neg p \Rightarrow p)$. This is equivalent to $p$ (only true when $p$ is true). Next, since $p$ is true, we evaluate $(p \Rightarrow \neg q) = (\neg p \vee \neg q)$. Since $p$ is true, $\neg p$ is false, so the implication becomes $\neg q$. Therefore, $(\neg p \Rightarrow p) \wedge (p \Rightarrow \neg q) = p \wedge \neg q$.
Correct Answer: 3