JEE Mains · Maths · STD 12 - 1. relation and function
The number of non-empty equivalence relations on the set \(\{1,2,3\}\) is :
- A \(6\)
- B \(5\)
- C \(7\)
- D \(4\)
Answer & Solution
Correct Answer
(B) \(5\)
Step-by-step Solution
Detailed explanation
Let \(R\) be the required relation \(\mathrm{A}=\{(1,1)(2,2),(3,3)\}\) (i) \(|\mathrm{R}|=3\), when \(\mathrm{R}=\mathrm{A}\) (ii) \(|\mathrm{R}|=5\), e.g. \(\mathrm{R}=\mathrm{A} \cup\{(1,2),(2,1)\}\) Number of \(R\) can be [3] (iii) \(\mathrm{R}=\{1,2,3\} \times\{1,2,3\}\)…
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