Question

prove: Let z be the set of integers and m a fixed positive integer. The relation of congruence modulo m in Z(set of integers) is an equivalence relation.

Answer 1

For a relation R, it is called an equivalence relation if it satisfies the following properties:
1. Reflexive: aRa
2. Symmetric: aRb \(\rightarrow\) bRa
3. Transitive aRb \(\wedge\) bRc \(\rightarrow\) aRc