Task 1. Determine $x \in \mathbb{Z}$ and $y \in \mathbb{Z}$ if $|x y|=6$
Solution. From $|x y|=6$ it follows that (i) $x y=6$ or (ii) $x y=-6$. From (i) it follows that

$$
(x, y) \in\{(1,6) ;(-1,-6) ;(2,3) ;(-2,-3) ;(6,1) ;(-6,-1) ;(3,2) ;(-3,-2)\}
$$

and from (ii) it follows that

$$
(x, y) \in\{(-1,6) ;(1,-6) ;(2,-3) ;(-2,3) ;(6,-1) ;(-6,1) ;(-3,2) ;(3,-2)\}
$$

The solution is the union of these two sets.