1. Problem: Simplify the logical expression $\sim[p \to (p \wedge \sim q)]$. 2. Recall that $p \to q$ is equivalent to $\sim p \vee q$. 3. So, $p \to (p \wedge \sim q) = \sim p \vee (p \wedge \sim q)$. 4. Negate the entire expression: $$\sim[p \to (p \wedge \sim q)] = \sim[\sim p \vee (p \wedge \sim q)] = p \wedge \sim(p \wedge \sim q)$$ 5. Apply De Morgan's law: $$p \wedge [\sim p \vee q]$$ 6. Simplify: $$ (p \wedge \sim p) \vee (p \wedge q) = \text{False} \vee (p \wedge q) = p \wedge q$$ 7. Final answer: $p \wedge q$. The correct choice is d) $p \wedge q$.