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The relation $R=\{(x, y): x, y \in \mathbb{Z}$ and $x+y$ is even $\}$ is:

JEE · Math · previous-year question

  1. A.reflexive and transitive but not symmetric
  2. B.reflexive and symmetric but not transitive
  3. C.an equivalence relationcorrect
  4. D.symmetric and transitive but not reflexive

Answer

C. an equivalence relation

Explanation

$R=\{(x, y): x, y \in z$ and $x+y$ is even $\}$ reflexive $x+x=2 x$ even symmetric of $x+y$ is even, then $(y+x)$ is also even transitive of $\mathrm{x}+\mathrm{y}$ is even $\& \mathrm{y}+\mathrm{z}$ is even then $x+z$ is also even So, relation is an equivalence relation.

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