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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 relationI had been asked this question in an interview.My enquiry is from Relations topic in division Relations of Discrete Mathematics

Answer»

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.



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