Problem 8. (Fun with truth tables)
(a) Form the truth table for $(P \implies Q) \land (P \lor Q)$
(b) Verify that $\lnot (P \lor Q)$ and $(\lnot P) \land (\lnot Q)$ are logically equivalent. That is: show that these two compound propositions have the same truth tables.
(c) Verify that both $\lnot (P \land \lnot Q)$ and $\lnot P \lor Q$ are logically equivalent to $P \implies Q$.
(d) (*) Form the truth table for $(P \land Q) \implies R$, where P, Q, and R are three different propositions. (Hint: your truth table should have 8 rows)