JEE Mains · Maths · STD 12 - 1. relation and function
Let \(R\) be a relation on \(N \times N\) defined by \((a, b) R\) (c, d) if and only if \(a d(b-c)=b c(a-d)\). Then \(R\) is
- A symmetric but neither reflexive nor transitive
- B transitive but neither reflexive nor symmetric
- C reflexive and symmetric but not transitive
- D symmetric and transitive but not reflexive
Answer & Solution
Correct Answer
(A) symmetric but neither reflexive nor transitive
Step-by-step Solution
Detailed explanation
\((a, b) R(c, d) \Rightarrow a d(b-c)=b c(a-d)\) Symmetric: \((c, d) R(a, b) \Rightarrow c b(d-a)=d a(c-b) \Rightarrow\) Symmetric Reflexive: (a, b) R \((a, b) \Rightarrow a b(b-a) \neq b a(a-b) \Rightarrow\) Not reflexive Transitive: \((2,3) R (3,2)\) and \((3,2) R (5,30)\) but…
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