JEE Mains · Maths · STD 12 - 1. relation and function
Consider the relations \(R_1\) and \(R_2\) defined as \(a R_1 b\) \(\Leftrightarrow a^2+b^2=1\) for all \(a, b, \in R\) and \((a, b) R_2(c, d)\) \(\Leftrightarrow a+d=b+c\) for all \((a, b),(c, d) \in N \times N\). Then
- A Only \(R_1\) is an equivalence relation
- B Only \(R_2\) is an equivalence relation
- C \(R_1\) and \(R_2\) both are equivalence relations
- D Neither \(R_1\) nor \(R_2\) is an equivalence relation
Answer & Solution
Correct Answer
(B) Only \(R_2\) is an equivalence relation
Step-by-step Solution
Detailed explanation
\(a R_1 b \Leftrightarrow a^2+b^2=1 ; a, b \in R\) (a, b) \(R_2(c, d) \Leftrightarrow a+d=b+c ;(a, b),(c, d) \in N\) for \(R_1\) : Not reflexive symmetric not transitive for \(R_2: R_2\) is reflexive, symmetric and transitive Hence only \(R_2\) is equivalence relation.
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