The probability that a relation R from {x, y} to {x, y} is both symmetric and transitive, is equal to :
JEE · Math · previous-year question
- A.$${5 \over {16}}$$correct
- B.$${9 \over {16}}$$
- C.$${11 \over {16}}$$
- D.$${13 \over {16}}$$
Answer
A. $${5 \over {16}}$$
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 $=5$ $\therefore \quad P_{r}=\frac{5}{16}$
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