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Math Help - Tautology-Need Help. Due Tomorrow

  1. #1
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    Tautology-Need Help. Due Tomorrow

    Hello! I need help with these 3 problem. When I am doing the steps I need to add the laws i used. Here it is:

    a.) Show that and are logically equivalent?

    b.) Show that and are logically equivalent?

    c.) Show that and are logically equivalent?

    Heres the laws I need to use:

    http://www.plu.edu/~sklarjk/245s07/logequiv.pdf
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  2. #2
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    It is just a matter of knowing the rules.
    \begin{gathered}<br />
  \left( {p \to q} \right) \wedge \left( {p \to r} \right) \hfill \\<br />
  \left( {\neg p \vee q} \right) \wedge \left( {\neg p \vee r} \right) \hfill \\<br />
  \neg p \vee \left( {q \wedge r} \right) \hfill \\<br />
  p \to \left( {q \wedge r} \right) \hfill \\ <br />
\end{gathered}
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  3. #3
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    Quote Originally Posted by Plato View Post
    It is just a matter of knowing the rules.
    \begin{gathered}<br />
  \left( {p \to q} \right) \wedge \left( {p \to r} \right) \hfill \\<br />
  \left( {\neg p \vee q} \right) \wedge \left( {\neg p \vee r} \right) \hfill \\<br />
  \neg p \vee \left( {q \wedge r} \right) \hfill \\<br />
  p \to \left( {q \wedge r} \right) \hfill \\ <br />
\end{gathered}
    Thanks Plato. I am starting to understand it alittle bit. But how does this:
    p V ( q ^ r )
    change to this:
    p → (q ^ r )
    ???
    What Law is that b/c as I am looking at my paper with the laws I don't see how it changes to the --> sign?
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  4. #4
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    Unfortunately the paper you supplied in the link does not have the material we need to do these questions.
    There is no consideration of implication
    .
    That is \left( {p \to q} \right) \equiv \left( {\neg p \vee q} \right) (p implies q is equivalent to not p or q).
    This is known in formal logic as Material Implication (Impl).
    Are there more pages in the text link?
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  5. #5
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    Quote Originally Posted by Grillakis View Post
    Thanks Plato. I am starting to understand it alittle bit. But how does this:
    p V ( q ^ r )
    change to this:
    p → (q ^ r )
    ???
    What Law is that b/c as I am looking at my paper with the laws I don't see how it changes to the --> sign?
    The law is: P v Q <====> (IS equivalent) ~P----->Q ,which by the way is not included in the page with the laws that you where given
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    I am sorry to get in the way ,you may not take into account my post
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  7. #7
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    Quote Originally Posted by Plato View Post
    Unfortunately the paper you supplied in the link does not have the material we need to do these questions.
    There is no consideration of implication
    .
    That is \left( {p \to q} \right) \equiv \left( {\neg p \vee q} \right) (p implies q is equivalent to not p or q).
    This is known in formal logic as Material Implication (Impl).
    Are there more pages in the text link?
    These 2 links are from my notes. I uploaded them using imageshack:

    ImageShack - Image Hosting :: law1jm0.png
    ImageShack - Image Hosting :: law2nt8.png

    I am doing it like this and this is what I see:
    ( p → q ) ^ ( p → r ) ≡ (p V q) ^ (p V r) Implication
    ≡ p V ( q ^ r ) 1st Distributive Law
    ≡ p → (q ^ r )
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  8. #8
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    Quote Originally Posted by archidi View Post
    I am sorry to get in the way ,you may not take into account my post
    archidi...thats alright. Any help from anybody is appreciated. Those notes I found online. I should have just uploaded the laws from my note, which i did now.
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  9. #9
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    Again unfortunately, neither of the new pages you supplied addresses Material Implication (Impl).
    That is \left( {p \to q} \right) \equiv \left( {\neg p \vee q} \right) .
    That is what you need to work these three problems.
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  10. #10
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    Quote Originally Posted by Plato View Post
    Again unfortunately, neither of the pages you supplied addresses Material Implication (Impl).
    That is \left( {p \to q} \right) \equiv \left( {\neg p \vee q} \right) .
    That is what you need to work these three problems.
    That stinks. Ok Plato I will try and work them again. Thanks for that other law.
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