JEE MAIN - Mathematics (2025 - 22nd January Evening Shift - No. 25)
Let $A=\{1,2,3\}$. The number of relations on $A$, containing $(1,2)$ and $(2,3)$, which are reflexive and transitive but not symmetric, is _________.
Answer
3
Explanation
Transitivity
$$(1,2) \in \mathrm{R},(2,3) \in \mathrm{R} \Rightarrow(1,3) \in \mathrm{R}$$
For reflexive $(1,1),(2,2)(3,3) \in R$
Now $(2,1),(3,2),(3,1)$
$(3,1)$ cannot be taken
(1) $(2,1)$ taken and $(3,2)$ not taken
(2) $(3,2)$ taken and $(2,1)$ not taken
(3) Both not taken
therefore 3 relations are possible.
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