Solution 3.1.8.1.

1. \(P \wedge Q\text{.}\)

2. \((\neg P \vee \neg R) \imp (Q \vee \neg R)\) or, replacing the implication with a disjunction first: \((P \wedge Q) \vee (Q \vee \neg R)\text{.}\)

3. \((P \wedge Q) \wedge (R \wedge \neg R)\text{.}\) This is necessarily false, so it is also equivalent to \(P \wedge \neg P\text{.}\)

4. Either Sam is a woman and Chris is a man, or Chris is a woman.