Prove this Tautology (No Truth Tables)

Posted by FSM on Super User See other posts from Super User or by FSM
Published on 2010-03-22T23:54:00Z Indexed on 2010/03/23 0:01 UTC
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logic

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math

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homework

This is for homework for my Discrete Math class.

I understand how to prove tautologies with a truth table. I'm having trouble figuring out how to do it without though.

I found this example in our text, but the solution is not provided. I was hoping someone could answer it as best they could so I could apply it to my other questions. Thanks!

! = not/invert
^ = and
V = or
-> = if then

[!P ^ (P V Q) ] -> Q

I also am completely lost for this question (I fear I'll be tested on something of this difficulty)

[ (P -> Q) ^ (Q -> R) ] -> (P -> R)

Thanks for the help all!

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