Question

Consider the relation: R’ (x, y) if and only if x, y>0  over the set of non-zero rational numbers,then R’ is _________

(a) not equivalence relation

(b) an equivalence relation

(c) transitive and asymmetry relation

(d) reflexive and antisymmetric relation

I got this question in unit test.

Question is taken from Types of Relations in division Relations of Discrete Mathematics

Answer 1

Right choice is (b) an equivalence relation

The explanation is: Reflexive: a, a>0

Symmetric: if a, b>0 then both must be +ve or -ve, which means b, a > 0 also exists

Transitive: if a, b>0 and b, c>0 then to have b as same number, both pairs must be +ve or -ve which implies a, c>0. Hence, R’ is an equivalence relation.