I've been working on this question on relations and finding at least one equivalent class. I'm done with finding the equivalence relation of this set, But i fail to understand the concept of classes, I looked at an example thrown by somebody on quora, where he explains this concept using a family tree where the siblings are related to each other, and instead of writing it all out, you could just write out the elements related in a single set, showing they're relations to each other.
In my question, x~y -> |x+2| = |y+2|, Prove that the relation defined on the set [-5, 5] is an equivalence relation and find a class.
(x~x): |x+2| = |x+2| = which is reflexive (a = a)
(y~x) -> (x~y) = |y+2| = |x+2| => |x+2| = |y+2| which is symmetric considering the ( a = b -> b = a)
(x~y) ^ (y ~ z) -> (x ~ z): |x+2| = |y+2| ^ |y+2| = |z+2| - > |x+2| = |z+2| since |y+2| = |z+2|, |x+2| = |z+2| and |x+2| = |z+2| - > |x+2| = |z+2| , and is transitive, and hence this is am equivalent relation. But how do i derive the class?
An explanation would help a lot.