Predicate Logic Truth Values

Question

I am given

universe of discourse: Z

predicate symbols: q

interpretation: $q(x,y) \iff x + y = 5$

There are two questions two questions which I don't understand:

i) $∀x.∃y.q(x,y)$ is true, I found it to be false

ii) $∀y.∃x.q(x,y)$ is true, I found it to be false

An explanation would be appreciated, thanks.

Answer 1

$∀x.∃y.q(x,y)$ is true because for any x you can choose y to be $(5-x)$ and $q(x,y)$ will be true. Same for the second question.