1. [(p-->q) ^ (q-->r)] --> (p-->r)
2. [p ^ (p-->q)]-->q
My book isn't exactly making it clear on how to do problems like these. Very frustrating. Can someone lead me in the right direction? All I know is that I'm supposed to use Logical Equivalences.
For the hypothetical syllogism (as opposed to categorical syllogism), it may be easier to prove that the negation is false. Note that ~(p -> q) = p /\ ~q. Take the negation of the whole formula and apply this rule to the outer implication (third from the left) and to p -> r. Replace the first two implications with disjunctions. Then use distributivity.