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Math Help - Logic proofs

  1. #1
    Junior Member
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    Logic proofs

    Hello,

    I have to solve this logic proof. I don't even know where to begin. It is supposed to resolve to true or false. Can anyone help?

    (P \equiv Q) \equiv P \lor Q \Rightarrow P \land Q

    Thank you for any help,
    DHS1
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  2. #2
    MHF Contributor
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    Quote Originally Posted by DHS1 View Post
    (P \equiv Q) \equiv P \lor Q \Rightarrow P \land Q
    What?

    Are you trying prove or disprove this:

    P\iff Q\equiv (P\lor Q)\land (P\land Q)
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  3. #3
    Junior Member
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    I am trying to prove this:

    P \equiv Q \equiv P \lor Q \Rightarrow P \land Q

    But since the equivalence operator is associative, there are two possible
    interpretations of formula:

    (P \equiv Q) \equiv P \lor Q \Rightarrow P \land Q<br />
    and
    <br />
P \equiv (Q \equiv P \lor Q \Rightarrow P \land Q)
    So I have to try to prove both of them. I only asked for help on one of them because I didn't want the thread to seem overwhelming and get skipped over.

    It is given that the operator precedence in this formula is:

    <br />
Logical AND ($\land$) and OR ($\lor$) -- highest<br />
    <br />
Implication ($\Rightarrow$)<br />
    <br />
Equivalence ($\equiv$) -- lowest

    I'm sorry but I don't really understand the logic in your last post. Does this information help?
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  4. #4
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    Never mind I solved it with the help of a friend. You can just delete this if you want.
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