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Math Help - Truth Tables

  1. #1
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    Truth Tables

    Are these two statements equivalent?

    When I simplify “not (not p and q) or (p and not r)” via rules I get “p or not q”.
    However the truth tables don’t seem to add up.

    Not (not p and q) or (p and not r)

    p q r not (not p and q) or (p and not r)

    1 1 1 1
    1 1 0 1
    1 0 1 1
    1 0 0 1
    0 1 1 0
    0 1 0 0
    0 0 1 1
    0 0 0 1




    p or not q

    p q p or not q
    1 1 1
    1 0 1
    0 1 0
    0 0 1



    Thanks
    Last edited by Gayelle; March 17th 2014 at 06:01 PM.
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  2. #2
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    Re: Truth Tables

    Where do the parentheses go? From what I see, Not(not p or q) or (p and not r) simplifies (to me) to:

    (p and not q) or (p and not r)

    Which then simplifies to

    p and (not q or not r)

    Then:

    p and not (q and r)

    So, I don't see how you simplified to "p or not q".
    Thanks from Gayelle
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  3. #3
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    Re: Truth Tables

    Quote Originally Posted by SlipEternal View Post
    Where do the parentheses go? From what I see, Not(not p or q) or (p and not r) simplifies (to me) to:

    (p and not q) or (p and not r)

    Which then simplifies to

    p and (not q or not r)

    Then:

    p and not (q and r)

    So, I don't see how you simplified to "p or not q".
    It was supposed to be "Not (not p and q) or (p and not r)".

    Sorry I'm not used to this.
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  4. #4
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    Re: Truth Tables

    $\begin{matrix}p & q & r & \neg(\neg p \wedge q)\vee(p\wedge \neg r) & p\vee \neg q \\ -- & -- & -- & --------- & ---- \\ T & T & T & T & T \\ T & T & F & T & T \\ T & F & T & T & T \\ T & F & F & T & T \\ F & T & T & F & F \\ F & T & F & F & F \\ F & F & T & T & T \\ F & F & F & T & T\end{matrix}$

    They look equivalent to me.
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  5. #5
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    Re: Truth Tables

    Ok got it.

    Thanks!
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