Predicate calculus - propositions

Let $\displaystyle p(x,y)$ denote the predicate $\displaystyle "x\leq y"$ and let $\displaystyle q(x,y)$ denote $\displaystyle "x<y"$ both with domain of definition N x N.

$\displaystyle \forall x \forall y \forall z ((p(x,y) \wedge p(y,z)) \rightarrow (p(x,z))$

$\displaystyle \forall x \forall y (\exists z(q(x,z) \wedge q(z,y)) \rightarrow (q(x,y))$

$\displaystyle \forall x \forall y (\exists z(q(x,z) \wedge q(z,y)) \leftrightarrow (q(x,y))$

$\displaystyle \exists x \forall y p(x,y)$

$\displaystyle \exists y \forall x p(x,y)$

This is a question I've been given. The question asks for me to translate them all into good English phrases. This I believe I have done correctly. It also asks me to say whether the proposition is true for each.

I have found that each is true, but I find this a bit suspicious, assuming at least one should be false, or maybe they're trying to throw me off (Itwasntme)

So I was wondering, does anyone disagree with my finding that all are true?