JEE Main 2022 (Online) 29th June Evening ShiftQuestion 1
The probability that a relation $R$ from $\{x,y\}$ to $\{x,y\}$ is both symmetric and transitive, is equal to
Sets, Relations and Function
Solution
Relations on $\{x,y\}$: $2^4=16$. Counting symmetric and transitive ones: $\emptyset$; $\{(x,x)\}$; $\{(y,y)\}$; $\{(x,x),(y,y)\}$; $\{(x,x),(y,y),(x,y),(y,x)\}$. ($\{(x,y),(y,x)\}$ alone fails transitivity as it needs $(x,x)$.) That is $5$. Probability $=5/16$. Option A.