(adsbygoogle = window.adsbygoogle || []).push({}); 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 triedmanydifferent 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?

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# Homework Help: Logic Proof

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