(Solved): Use truth tables to verify the following logical equivalences. Include a few words of explanation ...

Use truth tables to verify the following logical equivalences. Include a few words of explanation with your answers. (a) \( p \rightarrow q \equiv \sim p \vee q \) The truth table shows that \( p \rightarrow q \) and \( \sim p \vee q \) always do not always have the same truth values. Therefore they are are not logically equivalent. (b) \( \sim(p \rightarrow q) \equiv p \wedge \sim q \). (b) \( \sim(p \rightarrow q) \equiv p \wedge \sim q \). The truth table shows that \( \sim(p \rightarrow q) \) and \( p \wedge \sim q \) always do not always have the same truth values. Therefore they are are not logically equivalent.