Practice and Review 0

Date and Time: Friday, May 19 at 11 am

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• Recording Link (Passcode: i#0v@2Nv)

Problems

1. Prove \(a \leftrightarrow b \equiv (a \rightarrow b) \land (b \rightarrow a)\) using a truth table.

2. True or False: You can prove compound propositions \(X\) and \(Y\) are logically equivalent by showing \(X \leftrightarrow Y\) is a tautology. Explain your answer. (Hint, try this for the equivalence \(p \rightarrow q \equiv \neg p \lor q\))

3. True or False: \(((a \lor b) \oplus \neg b) \lor \texttt{True}\) always evaluates to \(\texttt{True}\) regardless of the values of \(a\) and \(b\). Explain your answer.