Question

Let R be a relation on a set of integers, which is represented by: a R...

Let R be a relation on a set of integers, which is represented by:
a R b if and only if a = 2 ^ k.b, for some integer k.
Check if the relation R is an equivalent relation!

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Answer #1

For a relation to be equivalence, it should be reflexive , symmetric and transitive.

A relation is said to be reflexive if aRa for all a in R.

That is, each integer in R should be related to itself. Like (1, 1) (2, 2).....

The given function is a = 2^k.b

Here we cannot have aRa possible. For example 1 2^k.b for any value of k and b.

Thus here since the given relation is not reflexive, it is not equivalent.

If you have any questions comment down. Please don't simply downvote and leave. If you are satisfied with answer, please? upvote thanks

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