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Math Help - Is the following a tautology?

  1. #1
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    Red face Is the following a tautology?

    Hi everyone!

    On my exam there is always a question like this:

    Is the following a tautology:

    [(r -> q) -> p] ↔ [r -> (q -> p)]

    I know how to solve this pretty easy by using a truth table or by just thinking a bit about the logic behind the statement. I was just wondering, is there some easier way to do this? I know about logical equivalence identities, but I find them difficult to apply to these kind of problems.

    Thanks to anyone who reads this!
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  2. #2
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    Re: Is the following a tautology?

    Quote Originally Posted by Nora314 View Post
    Hi everyone!
    Is the following a tautology:
    [(r -> q) -> p] ↔ [r -> (q -> p)]
    Say r\equiv F,~q\equiv T,~\&~p\equiv F. SO?

    The first is \neg \left( {\neg r \vee q} \right) \vee p.

    The second is \neg r \vee \left( {\neg q \vee p} \right)
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