Let $\mathcal{R}$ be a relation on $\mathbb{Z}$ given by
$\mathcal{R}=\{(a, b) \in \mathbb{Z} \times \mathbb{Z}: 3 \mid(a-b) \quad \text { or } \quad 2 \mid(a+b)\} .$
Then $\mathcal{R}$ is

• A

  symmetric and transitive but not reflexive
• Correct answer
  B

  reflexive and symmetric but not transitive
• C

  reflexive and transitive but not symmetric
• D

  an equivalence relation

Hence, the correct answer is option: 'B'.