Thread: how Z (integer) is an equivalence relation.

1. how Z (integer) is an equivalence relation.

Prove that the relation on Z (integer) define by a~b iff a – b is divisible by 5. is an equivalence relation.

Can anybody help me on this

2. Re: how Z (integer) is an equivalence relation.

Originally Posted by rcs
Prove that the relation on Z (integer) define by a~b iff a – b is divisible by 5. is an equivalence relation.

Can anybody help me on this
Prove that ~ is reflexive relation, symmetric and transitive.

3. Re: how Z (integer) is an equivalence relation.

Another little help:

Reflexive: For all $a\in\mathbb{Z}$ we have

$a-a=0=5\cdot 0$ that is, $a-a$ is divisible by $5$ which means that $a\sim a$

Try the rest.