The given relation is and is divisible by 5 .

We shall prove that is reflexive, symmetric and transitive.

(i) is reflexive as for any , we have and 0 is divisible by 5

is divisible by 5

is reflexive.

(ii) is symmetric As , where

is divisible by 5 [By definition of R ]

for some

is also divisible by 5

is symmetric.

(iii) is transitive As , where

is divisible by 5

for some

Again, for where,

is divisible by 5

for some

Now,

is divisible by 5 for some

is transitive.

Since, is reflexive, symmetric and transitive.

Therefore, it is an equivalence relation.

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