What is the difference and how can I write these two statements in both forms?
Not in every hole lives a pigeon.
Some pigeon lives in more than one hole.
For the first statement I have $∀h∀p [LivesIn(p, h)]$ but I am not sure how to express this in the universal form.
I am not sure how to express the second statement, because it says "more than one", so a for all wouldn't make sense (at least from what I understand (which is very little))
Also, if you combine a for all and a there exists then what is it, existential or universal? If anybody can help clear the air on these problems for me I would be extremely grateful.