# Homework Help: Logic - Switching quantifiers

1. Feb 1, 2010

### rokimomi

1. The problem statement, all variables and given/known data

Determine whether $$\exists$$x$$\forall$$y[p(y) --> q(x)] is equivalent to $$\forall$$y$$\exists$$x[p(y) --> q(x)], justify your answer with a proof.

2. Relevant equations

3. The attempt at a solution

I know that when you switch quantifiers in something like P(x,y), the meaning changes and it is not equivalent but how about here where the variables are again separated. My intuition is telling me they are equivalent, or rather I should say I can't think of any proof that would falsify this.

Likewise, I cant think of how to prove this either. Would I have to do something along the lines of exploring all true false values for the given situations?