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Question

Let $R$ be a relation on $\mathbb{R}$, given by $R=\{(a, b): 3 a-3 b+\sqrt{7}$ is an irrational number $\}$. Then $R$ is

an equivalence relation
reflexive and symmetric but not transitive
reflexive and transitive but not symmetric
reflexive but neither symmetric nor transitive

Solution

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