1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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

    User Avatar
    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).
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook