Determine the Truth Value of each of these Statements? 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$
True
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.
Thank you.

*

*False. Take $x=2$. Then there is no integer $y$ such that $2 = 3y+1$, for then $3y = 1$. Remember, it has to work for all $x$, not just some.

*True. Take any negative number for $x$. Then $y^2$ will always be greater than $x$. So yes, there is some $x$ such that $y^2 >x$ for all $y$.
