The probability that a relation R from {x, y} to {x, y} is both symmetric and transitive, is equal to :
Solution
Total number of relations $=2^{2^{2}}=2^{4}=16$
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Relations that are symmetric as well as transitive are
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$\phi,\{(x, x)\},\{(y, y)\},\{(x, x),(x, y),(y, y),(y, x)\},\{(x, x),(y, y)\}$
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$\therefore \quad$ favourable cases $=5$
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$\therefore \quad P_{r}=\frac{5}{16}$
About this question
Subject: Mathematics · Chapter: Probability · Topic: Classical and Axiomatic Probability
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