Ok guys. Here's a brain-drainer. Show:

[For every x P(x)] OR [For every x Q(x)]

and

For every[ P(x) OR Q(x) ]

are NOT logically equivilent.

This is really giving me sleep problems. I can get this to work with AND (instead of OR). You simply Let P(x) = "x is even" and Q(x) = "x is odd" so therefor, the first is true, but the second is not (because a number can't be even AND odd).

So how do you do it for OR?