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Set Theory Logic Question

  1. Feb 17, 2014 #1
    1. The problem statement, all variables and given/known data
    In each of the two following open sentences P(x) and Q(x) over a domain S are given.
    Determine all ##x \in S## for which P(x) → Q(x) is a true statement.

    ## P(x): x \in [-1, 2]; Q(x): x^{2} \leq 2; S=[-1,1] ##

    2. Relevant equations
    According to truth values for →:
    a b a-> b
    0 0 1
    0 1 1
    1 0 0
    1 1 1
    3. The attempt at a solution
    If I can prove that P is False, then I will always get a T value for ->
    Can I just say ## x \in [-1,1] ##, this would literally mean that statement P is false.
    Could this count?
     
  2. jcsd
  3. Feb 18, 2014 #2
    Would this mean that the statement is true vacuously?
     
  4. Feb 18, 2014 #3

    vela

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    Is there any ##x \in S## such that P(x) is false?
     
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