A relation defined on set \(A=\{1,2,3,4\}\), then how many minimum ordered pairs are added to \(R=\{(1,2),(2,3),(3,3)\}\…
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A relation defined on set \(A=\{1,2,3,4\}\), then how many minimum ordered pairs are added to \(R=\{(1,2),(2,3),(3,3)\}\) so that it becomes equivalence relation?
[JEE Main 2025]
✓ Correct answer: c)
7
Explanation
For equivalence it must be transitive, symmetric and reflexive all.
For reflexive \(\rightarrow \quad(1,1),(2,2),(4,4)\)
For symmetric \(\rightarrow \quad(2,1),(3,2)\)
For transitive \(\rightarrow \quad(1,3),(3,1)\)
Total 7 pairs has to be added to make it's an equivalence relation.
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