Let R be a relation on the set of all integers such that aRb if and...

Let R be a relation on the set of all integers such that aRb if and only if 3a − 5b is even. Tell if R is an equivalence relation. Justify your answer. (Hint: 3b − 5a = 3a − 5b + 8b − 8a)

Expert Solution

It is a simple proof by just remembering that even multiples of integers are even integers, and sums and differences of even integers are also even integers.

So, we have proved the relation R on integers to be REFLEXIVE, SYMMETRIC and TRANSITIVE.

Therefore, R is an equivalence relation on the set of integers.

Colby Messinger answered 5 months ago

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Let R be a relation on the set of all integers such that aRb if and...

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