Question 325454
*[Tex \LARGE \sim (\sim p \rightarrow \sim q) \equiv \sim (\sim(\sim p) \vee \sim q) \equiv \sim (p \vee \sim q) \equiv \sim p \wedge \sim(\sim q) \equiv \sim p \wedge q]



So in short, *[Tex \LARGE \sim (\sim p \rightarrow \sim q) \equiv \sim p \wedge q]



This means that *[Tex \LARGE \sim (\sim p \rightarrow \sim q) \not{\equiv} p \rightarrow q]



So the statement is false.



Notice that if p is false and q is false, then *[Tex \LARGE \sim (\sim p \rightarrow \sim q)] is false, but *[Tex \LARGE p \rightarrow q] is true



So this shows that the two expressions do not have the same truth values.