JEE MAIN - Mathematics (2022 - 29th June Evening Shift - No. 10)
The probability that a relation R from {x, y} to {x, y} is both symmetric and transitive, is equal to :
$${5 \over {16}}$$
$${9 \over {16}}$$
$${11 \over {16}}$$
$${13 \over {16}}$$
Explanation
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 $=5$
$\therefore \quad P_{r}=\frac{5}{16}$
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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