JEE Main 2025 (Online) 8th April Evening ShiftQuestion 1
Let $A=\{0,1,2,3,4,5\}$. Let $R$ be a relation on $A$ defined by $(x,y)\in R$ if and only if $\max\{x,y\}\in\{3,4\}$. Then among the statements
$(S_1)$ : The number of elements in $R$ is $18$, and
$(S_2)$ : The relation $R$ is symmetric but neither reflexive nor transitive
Sets, Relations and Function
Solution
Pairs with $\max=3$: $2\cdot3+1=7$; with $\max=4$: $2\cdot4+1=9$. So $|R|=16\ne18$: $S_1$ false. Symmetric yes (max symmetric). Not reflexive: $(0,0)\notin R$. Not transitive: $(0,3),(3,0)\in R$ but $(0,0)\notin R$. $S_2$ true. Option D.