Question

Suppose a relation R = {(3, 3), (5, 5), (5, 3), (5, 5), (6, 6)} on S = {3, 5, 6}. Here R is known as _________

(a) equivalence relation

(b) reflexive relation

(c) symmetric relation

(d) transitive relation

I had been asked this question in an interview.

My enquiry is from Relations topic in division Relations of Discrete Mathematics

Answer 1

The correct choice is (a) equivalence relation

To explain: Here, [3] = {3, 5}, [5] = {3, 5}, [5] = {5}. We can see that [3] = [5] and that S/R will be {[3], [6]} which is a partition of S. Thus, we can choose either {3, 6} or {5, 6} as a set of representatives of the equivalence classes.