1.Relation and Function
medium

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

A

$\frac{5}{16}$

B

$\frac{9}{16}$

C

$\frac{11}{16}$

D

$\frac{13}{16}$

(JEE MAIN-2022)

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. $=\frac{5}{16}$

Standard 12
Mathematics

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