Question

Show that the relation r on z defined by r={(a, b):|a-b|is even} is an equivalence relation.

Answer 1

In the attachments I have answered this problem.

The solution is simple and easy to understand.

See the attachment for detailed solution.

Answer 2

Question:

Let R={(a,b):a,b€N and a<b} Show that R is a binary realtion on N,Which is neither Reflexive nor symmetric,Show R is transitive