Proof Writing & Problem Solving · Challenge problem

Let $x$ and $y$ range over the positive integers, and let $D(x, y)$ mean "$x$ divides $y$". How many of these six statements are TRUE?

(1) $\forall x\, \forall y\, D(x, y)$  (2) $\exists x\, \exists y\, D(x, y)$  (3) $\forall x\, \exists y\, D(x, y)$

(4) $\exists y\, \forall x\, D(x, y)$  (5) $\forall y\, \exists x\, D(x, y)$  (6) $\exists x\, \forall y\, D(x, y)$