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Math Help - Proving Logical Equivalences

  1. #1
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    Proving Logical Equivalences

    I know how to use truth tables to prove they are equivalent, but how do I prove symbolically using the rules of logic?

    Show that (p -> ((not q) and r)) and (not p or (not (r implies q))) are logically equivalent:


    (I wrote out some of the symbols for keys that I do not have)

    I have no idea what to do now. Any help would be appreciated! Thank you!
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  2. #2
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    Re: Proving Logical Equivalences

    What rules of logic do you know? For example do you know that "not (r implies q)" is equivalent to "r and (not q)"?
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  3. #3
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    Re: Proving Logical Equivalences

    I was using conditional statements where p implies (q and r) is equivalent to ( p implies q) and (p implies r)

    I started with the left hand side:

    p implies (not q and r)

    conditional statement: (p implies not q) and (p implies r)

    that is what I have so far. I don't even know if that is the right step.
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