So I have a questions about nested quantifiers that I am really not catching on.
I have E(x) = x is even and P(x) = x is prime.
The questions is asking if the following holds for :
1) natural numbers
2) even numbers
3) integers
4) rational number
∀x∃y, x^2 = y
Why isn't the answer natural numbers, even numbers, and rational numbers??
I also need some more clarification for universal quantifiers and existential quantifiers.