What would be the truth value for the following two quantifiers if n and m are both integers? I have trouble proving each of these statements. I appreciate any help you can provide!
a) $\forall n\; \exists m\; (n^2 < m)$
b) $\exists n\; \forall m\; (n < m^2)$
Best Answer
The first is true. Just let $m = n^2 + 1$.
The second is also true. Let $n = -1$. For any $m$, $m^2 \geq 0$, and $n < 0$.