(a) The expression can be false only if both terms are false, but this would imply, on the one hand, that $P=T$ and $Q=F$ , and, on the other hand, that $Q=T$ and $P=F$ . Hence, this is a tautology.

(b) The first expression is false iff $P\wedge Q$ is true and $R$ is false, the second is false iff both terms are false iff $P$ is true and $Q$ is true and $R$ is false. Therefore, not only the first formula tautologically implies the second one, but also they are tautologically equivalent. Another way to see this: $((P\wedge Q)\rightarrow R)$ is tautologically equivalent to $((\neg(P\wedge Q))\vee R)$ is tautologically equivalent to $(((\neg P)\vee(\neg Q))\vee R)$ is tautologically equivalent to $(((\neg P)\vee R)\vee((\neg Q)\vee R))$ is tautologically equivalent to $((P\rightarrow R)\vee(Q\rightarrow R))$ .