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Truth values of nested quantifiers

  1. Oct 28, 2012 #1
    1. The problem statement, all variables and given/known data

    Let P(x,y) denote the sentence 2x +y = 1
    What is the truth value of ∃x∃xP(x,y) where the domain of x, y is the set of all integers.


    2. Relevant equations



    3. The attempt at a solution

    This problem doesn't make sense to me. Doesn't one of the variables need to be a y in ∃x ∃xP(x,y)? In other words shouldn't the proposition be ∃x∃yP(x,y) or something similar?

    Could this simply be a typo?

    Thanks for any suggestions.
     
  2. jcsd
  3. Oct 30, 2012 #2
    It's a typo. Two quantifiers in a row on the same variable is the same as one. It's a bit like Porky Pig "There is a.. There is a... I say, there is an x..."
     
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