JEE Main 2025 Jan 22 Shift 2, Mathematics Q25: Relations
JEE Main2025Jan 22, Shift 2Mathematics
Q.
Let . The number of relations on , containing and , which are reflexive and transitive but not symmetric, is ______.
Correct answer: 3
Solution
$ \textbf{Transitivity} $
$ (1,2)\in R,\ (2,3)\in R \Rightarrow (1,3)\in R $
$ \text{For reflexivity } (1,1),\ (2,2),\ (3,3)\in R $
$ \text{Now }(2,1),\ (3,2),\ (3,1) $
$ (3,1)\text{ cannot be taken.} $
$ (1)\ (2,1)\text{ taken and }(3,2)\text{ not taken} $
$ (2)\ (3,2)\text{ taken and }(2,1)\text{ not taken} $
$ (3)\ \text{Both not taken} $
$ \therefore\ \text{3 relations are possible.} $
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