JEE Mains · Maths · STD 12 - 1. relation and function
Let \(R\) be a relation on \(R\), given by \(R=\{(a, b): 3 a-3 b+\sqrt{7}\) is an irrational number \(\}\). Then \(R\) is
- A Reflexive but neither symmetric nor transitive
- B Reflexive and transitive but not symmetric
- C Reflexive and symmetric but not transitive
- D An equivalence relation
Answer & Solution
Correct Answer
(A) Reflexive but neither symmetric nor transitive
Step-by-step Solution
Detailed explanation
Check for reflexivity: As \(3(a-a)+\sqrt{7}=\sqrt{7}\) which belongs to relation so relation is reflexive Check for symmetric: Take \(a=\frac{\sqrt{7}}{3}, b=0\) Now \((a, b) \in R\) but \((b, a) \notin R\) As \(3(b-a)+\sqrt{7}=0\) which is rational so relation is not symmetric.…
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