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Logic Proof

  1. Jan 17, 2012 #1
    1. The problem statement, all variables and given/known data

    Prove ∃x(P(x) → ∀y(P(y))).

    2. Relevant equations

    3. The attempt at a solution

    ∃x(P(x) → ∀y(P(y))) is equivalent to ∃x(¬P(x) ∨ ∀y(P(y))).

    This exercise is found in a section on "proofs involving disjunctions." I have tried many different ways to solve this and have a feeling I am not approaching it the right way. Perhaps I am not considering clever enough exhaustive cases? Can anyone direct me in the proper way to begin?
  2. jcsd
  3. Jan 17, 2012 #2
    This is an exercise from "How to prove it" right?:biggrin:

    I'm having troubles with this one too.

    I've tried a proof by contradiction, i think i proved it but I'm not so sure.
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