JEE Main · 2026 · 23 Jan 2026 · Shift 1 · Sets Relations and Functions

Counting the ordered pairs with $2x+y\le 2$: for $x=-2$ and $x=-1$ every $y\in A$ works ($7$ each), for $x=0$ the values $y\in \{-2,-1,0,1,2\}$ work ($5$), for $x=1$ the values $\{-2,-1,0\}$ ($3$), for $x=2$ only $y=-2$ ($1$), and $x=3,4$ give none. Thus $l=7+7+5+3+1=23$. Reflexivity needs every $(x,x)$; since $3x\le 2$ holds only for $x=-2,-1,0$, the pairs $(1,1),(2,2),(3,3),(4,4)$ are absent, so $m=4$. Symmetry needs the mirror of each pair whose reverse violates $2y+x\le 2$; these are $(3,-2),(4,-2),(2,-1),(3,-1),(4,-1),(0,2)$, six in all, so $n=6$. Therefore $l+m+n=23+4+6=33.$