JEE Main · 2025 · 07 Apr 2025 · Shift 1 · Sets Relations and Functions

A reflexive relation on $\{1,2,3\}$ must contain $(1,1),(2,2),(3,3)$, and here also $(1,2)$, leaving room for at most two further ordered pairs. To keep the relation from being symmetric, the pair $(2,1)$ must be excluded. Taking no further pair gives one relation. Adding exactly one pair, only $(1,3)$ or $(3,2)$ preserves transitivity, giving two more. Adding two pairs, the transitive possibilities are $\{(1,3),(2,3)\}$, $\{(1,3),(3,2)\}$ and $\{(3,1),(3,2)\}$, giving three more. In all there are $1+2+3=6$ such relations.