For each of the following relations, does it satisfy each of six properties (reflexive, irreflexive, symmetric, asymmetric, antisymmetric, and transitive) or not? If your answer is Yes you will need to prove; otherwise you will need to provide one counterexample.

1. The divide relation on integers, i.e., (Z, |).

Explanation of the relation: x|y iff x divides y (e.g., 2|10, but not 3|10).