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Truth Values of Nested Qualifiers

  1. Oct 28, 2012 #1
    This problem doesn't make sense to me. Here it is:

    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.

    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 28, 2012 #2

    haruspex

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    Yes, there needs to be a quantifier for y.
    My guess is that it ought to say [itex]\forall x\exists y:P(x,y) [/itex], or possibly with the quantifiers swapped (with a very different answer).
     
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