The Boolean expression $$(p \wedge \sim q) \Rightarrow (q \vee \sim p)$$ is equivalent to:

We need to simplify $$(p \wedge \sim q) \Rightarrow (q \vee \sim p)$$.

Using the equivalence $$A \Rightarrow B \equiv \sim A \vee B$$, we write: $$\sim(p \wedge \sim q) \vee (q \vee \sim p).$$

By De Morgan's law, $$\sim(p \wedge \sim q) = \sim p \vee q$$. Substituting: $$(\sim p \vee q) \vee (q \vee \sim p) = \sim p \vee q.$$

The expression $$\sim p \vee q$$ is precisely the conditional $$p \Rightarrow q$$.

Therefore $$(p \wedge \sim q) \Rightarrow (q \vee \sim p)$$ is equivalent to $$p \Rightarrow q$$.