WBJEE · Maths · Sets and Relations
Let \(R\) be a relation defined on the set \(Z\) of all integers and \(x R y,\) when \(x+2 y\) is divisible by 3 , then
- A \(R\) is not transitive
- B \(A\) is symmetric only
- C \(R\) is an equivalence relation
- D \(A\) is not an equivalence relation
Answer & Solution
Correct Answer
(C) \(R\) is an equivalence relation
Step-by-step Solution
Detailed explanation
Reflexivity For reflexive \((x, x) \in R .\) \(x+2 x=3 x\) which is divisible by 3. \(\Rightarrow\) xRx \(\in R\) Hence, xRy is reflexive. Symmetric Let \(x+2 y=3 \lambda\) \(\Rightarrow \quad x=3 \lambda-2 y\)…
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