(10 pts) a relation r is defined on the set z by "a r b if a - b is divisible by 5" for a, b e z. examine if r is an equivalence relation on z.

Yes

Step-by-step explanation:

Given that a relation R is defined on the set Z by "a R b if a - b is divisible by 5

for a, b in the set of integers.

Reflexive:

We have

for any a,

i.e. (a,a) is related. Hence reflexive

ii) Symmetric:

If a-b is divisible by 5, then b-a is also divisible by 5.  Hence symmetric

iii) Transitive

If

adding we get

Hence R is transitive

It follows that R is an equivalence relation on Z

the answer is c. ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀