The number of relations on the set $\mathrm{A}=\{1,2,3\}$ containing at most 6 elements including $(1,2)$, which are reflexive and transitive but not symmetric, is ________

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Aicharya · Accepted Answer

$\begin{aligned} & A=\{1,2,3\} \ & (1,1),(2,2),(3,3),(1,2) \in R \end{aligned}$ Remaining elements are $(2,1),(2,3),(1,3),(3,1),(3,2)$ (1) If relation contains exactly 4 elements = 1 way (2) if relation contains exactly 5 elements It can be $(1,3),(3,2) \Rightarrow 2$ ways (3) If relation contain exactly 6 elements It can be $((2,3),(1,3)),((1,3),(3,2)),((3,1),(3,2))$ $\Rightarrow 3$ ways. Total $=6$ ways

The number of relations on the set $\mathrm{A}=\{1,2,3\}$ containing at most 6 elements including $(1,2)$,…

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