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  4. The probability that a relation R from x , y to x , y is both symmetric and transitive, is equal to:

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Q. The probability that a relation $R$ from $\{ x , y \}$ to $\{ x , y \}$ is both symmetric and transitive, is equal to:

JEE MainJEE Main 2022Probability - Part 2

Solution:

Total no. of relations $=2^{2 \times 2}=16$
Fav. relation $=\phi,\{( x , x )\},\{( y , y )\},\{( x , x )( y , y )\}$
$\{(x, x),(y, y),(x, y)(y, x)\}$
Prob. $=\frac{5}{16}$