# Math Help - Equivalence Relation Identification

1. ## Equivalence Relation Identification

Are the following equivalence relations?

x~y if x < y NO

x~y if x <= y NO

x~y if |x| = |y| YES

x~y if x =/ y NO

x~y if xy > 0 NO

x~y if x|y or y|x YES

What are the equivalence classes for the ones that are? Thanks!

2. Originally Posted by jstarks44444
Are the following equivalence relations?

x~y if x < y NO

x~y if x <= y NO

x~y if |x| = |y| YES

x~y if x =/ y NO

x~y if xy > 0 NO

x~y if x|y or y|x YES

What are the equivalence classes for the ones that are? Thanks!
Do $x,y\in\mathbb{Z}\text{?}$