Check whether each set of formulas is consistent or not, and justify your answer with a truth assignment or truth table as appropriate. (a) {AB,AB} (b) {PQ,P,Q} (c) {HE,GH,G} 1. For each of the following pairs of formulas, decide if they are logically equivalent, and justify your answer with a truth assignment or truth table as appropriate. (a) PQ and (PQ)(PQ) (b) AB and BA 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 AB is BA. 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 AB is BA. While the converse of an implication is not equivalent to the original conditional (A BA), it turns out that the contrapositive of an implication is equivalent to the original (ABBA) (a) Prove that an implication is not logically equivalent to its converse. In other words, find a counterexample that proves AB is not logically equivalent to BA. (b) Prove that an implication is logically equivalent to its contrapositive. In other words, show that every truth assignment gives the same outcome for AB as it does for BA