PS02: More Propositional Logic

1. Is the following proposition satisfiable? Explain. $$(p \lor q \lor \neg r) \land (p \lor \neg q \lor \neg s) \land (p \lor \neg r \lor \neg s) \land (\neg p \lor \neg q \lor \neg s) \land (p \lor q \lor \neg s)$$

Rewrite each of the following compound propositions so that each variable occurs at most once. Prove that your proposition is equivalent to the original using a truth table.

1. $\neg p \land (p \lor q)$
2. $p \Rightarrow (p \land q \land r)$
3. $((p \land q) \Rightarrow (p \lor q)) \Rightarrow (q \Rightarrow r)$

Do the following problems from the book, listed on pages 332–335.

1. 3.33
2. 3.40 (and justify your answer)
3. 3.44
4. 3.67
5. 3.68
6. 3.69
7. 3.71
8. 3.95
9. 3.101
10. 3.105
11. 3.106