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DISCRETE MATH: Determine if two statements are logically equivalent

  1. Jan 18, 2007 #1
    1. The problem statement, all variables and given/known data

    Determine whether [tex]\forall\,x\,(P(x)\,\longleftrightarrow\,Q(x))[/tex] and [tex]\forall\,x\,P(x)\,\longleftrightarrow\,\forall\,x\,Q(x)[/tex] are logically equivalent. Justify your answer.

    2. Relevant equations

    [tex]P\,\longleftrightarrow\,Q[/tex] is only TRUE when both P and Q are TRUE or FALSE.

    3. The attempt at a solution

    No, I don't think the two statements are logically equivalent, but I have trouble trying to "justify" my answer.

    Set P and Q as always TRUE.

    Both statements are equivalent, but if you set P and Q to always FALSE, then the statements are no longer equivalent.

    Does this seem logical:rolleyes:
  2. jcsd
  3. Jan 18, 2007 #2

    matt grime

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    Science Advisor
    Homework Helper

    Not very. Why not just write things out properly? As in for all z in S then P(z)
    is just the same as z in S implies P(z).
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