I need help determining the truth value of each of these statements if the domain of each variable consists of all integers. Justify your answer.
- $\forall x\exists y (x = 3y + 1)$
- $\exists x\forall y (y^2 > x)$
If I take $x$ as $-5$ and take $y$ as $-2$ then it would be
$ -5 = 3(-2) + 1 $
$ -5 = -5$
So what I did is true only if i take those values. If I take $x$ as $-5$ and $y$ as $-5$ then it wouldn't equal so its False
So I am just confused on how to do these type of questions so can someone help me figure it out.