I am doing my first maths class since high school three years ago and I'm having trouble at getting my head around the abstraction of equivalence relations.
The following table gives a list of 6 different relations.
a) Which of the relations are equivalence relations? Mark anXin the column under “is equivalence relation?”for those which are equivalence relations.
b) For those which are equivalence relations, give an example of an equivalence class (i.e., choose an elementxof the set, and write a list of all the elements equivalent tox, or a formula for all the elements if this isan inﬁnite set).
c) For those which are equivalence relations, in the last column of the table, write down the number ofequivalence classes (this could be inﬁnite.)
Each relation in this table is a relation on a given set, listed under “set”.
Set / Relation
1. R /aRb ⇐⇒ a−b is negative
2. Z / aRb ⇐⇒ a−b is even
3. R / aRb ⇐⇒ |a|=b
4. R/ aRb ⇐⇒ |a|=|b|
5. R/aRb ⇐⇒ |a|b=a|b|
6.Z/aRb⇐⇒|a| − |b| is even
Ok - What I think
To be an equivalence relation the relation on the set needs to be reflexive, symmetric and transitive. I am having trouble with understanding how the reflexive requirement applies on any of these
1. Every relation will be in Z so it is reflexive? Not symmetric. Not transitive
2. Reflexive, Symmetric, transitive. 2 equivalence classes  and 
3. Reflexive, not symmetric, not transitive.
4. Reflexive, Symmetric, transitive. Equivalence classes ,,,...[,oo]
5. Reflexive, not symmetric, not transitive
6. The same as 2.
Any help/advice is greatly appreciated.