The probability that a relation R from x, y to x, y is both symmetric and transitive, is e…

Question

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

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

$	herefore \quad$ favourable cases $=5$

$	herefore \quad P_{r}=\frac{5}{16}$

Solutions · 1