QJEEM22Ma3690: JEE Main 2022 Mathematics - Class 12 JEEM22Ma3690 Solution: The probability that a relation R from {x, y} to {x, y} is both …

Question

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

Accepted Answer

Total number of relations

=2^{2^{2}}=2^{4}=16

Relations that are symmetric as well as transitive are

\phi,\{(x, x)\},\{(y, y)\},\{(x, x),(x, y),(y, y),(y, x)\},\{(x, x),(y, y)\}

\therefore \quad

favourable cases

=5

\therefore \quad P_{r}=\frac{5}{16}

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