JEE Mains · Maths · STD 12 - 1. relation and function
Let \(R\) be a relation defined on \(N\) as a \(R\) b is \(2 a+3 b\) is a multiple of \(5, a, b \in N\). Then \(R\) is
- A not reflexive
- B transitive but not symmetric
- C symmetric but not transitive
- D an equivalence relation
Answer & Solution
Correct Answer
(D) an equivalence relation
Step-by-step Solution
Detailed explanation
\(a R a \Rightarrow 5 a\) is multiple it 5 So reflexive \(a R b \Rightarrow 2 a +3 b =5 \alpha\), Now b R a \(2 b+3 a=2 b+\left(\frac{5 \alpha-3 b}{2}\right) \cdot 3\) \(=\frac{15}{2} \alpha-\frac{5}{2} b=\frac{5}{2}(3 \alpha-b)\) \(=\frac{5}{2}(2 a+2 b-2 \alpha)\)…
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