JEE Main · 2004 · 24 Apr 2004 · Offline · Sets Relations and Functions

A quick scan of the pairs settles this. For a function each input must have a single output, but here $2$ is sent to both $4$ and $3$, so $R$ is not a function. Reflexivity would need $(1,1),(2,2),(3,3),(4,4)$, none of which appear, so $R$ is not reflexive. Symmetry fails the moment we find one pair whose reverse is missing: $(2,3)\in R$ while $(3,2)\notin R$, so $R$ is not symmetric. Transitivity also breaks, since $(2,4)$ and $(4,2)$ are both present yet $(2,2)$ is absent. The one property that genuinely describes $R$ is that it is not symmetric.