5. The converse of an implication (such as AB) is the implication you get by switching the positions of the premise (A in our example) and conclusion (B). So the converse of A B is B A.

The contrapositive of an implication is the what you get by switching the premise and conclusion and replacing them with their negations. So the contrapositive of A B is B A. While the converse of an implication is not equivalent to the original conditional (A B 6 B A), it turns out that the contrapositive of an implication is equivalent to the original (A B B A).

(a) Prove that an implication is not logically equivalent to its converse. In other words, find a counterexample that proves A B is not logically equivalent to B A.

(b) Prove that an implication is logically equivalent to its contrapositive. In other words, show that every truth assignment gives the same outcome for A B as it does for B A.