Tautological implication Determine whether or not $((P\land Q)\implies R)$ tautologically implies $((P\implies R)\lor (Q\implies R))$ How do I determine that $((P\land Q)\implies R)$ tautologically implies $((P\implies R)\lor(Q\implies R))$? The problem is not to show equivalence, but to determine whether one formula tautologically implies another, and I'm confused about the difference. Any clarification would be appreciated.

A formula A either will tautologically imply another formula B, or it will not do so. If A does NOT tautologically imply B, then there exists some truth-value assignment such that A holds true, and B qualifies as false. Suppose ((P→R)∨(Q→R)) false. Then, (P→R)qualifies as a false, and so does (Q→R). Thus, P qualifies as true, Q qualifies as true, and R qualifies as false. If those conditions hold, then ((P∧Q)→R) qualifies as false also. So, it is not the case that A does not tautologically imply B. Thus, because of the content of the initial sentence, ((P∧Q)→R) tautologically implies ((P→R)∨(Q→R)).