On the set of integers

MATHEMATICS · Subjective · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

On the set of integers Z\mathbb Z, a relation RR is defined by a R b  ⟺  a+b is odd.a \thinspace R \thinspace b \iff a+b \text{ is odd}. Examine whether RR is reflexive, symmetric and transitive, and state whether it is an equivalence relation. Give justification for each property.

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