Question

8. Let R be the relation defined on 0, (set of non-zero rational numbers) defined by
R = {(a, b) : a, b e Qob
Check the relation R for reflexivity, symmetricity and transitivity,​

Answer 1

Answer:

Since a−a=0 and 0 is an even integer

(a,a)∈R

∴ R is reflexive.

(ii) If (a−b) is even, then (b−a) is also even. then, if (a−b)∈R,(b,a)∈R

∴ The relation is symmetric.

∴ R is transitive.

Since R is reflexive, symmetric and transitive, it is an equivalence relation.