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  • The probability that a relation  from <img alt="\mathrm{\{x, y\} \text { to }\{x, y\}}" src=

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

Option: 1

\frac{5}{16} \\


Option: 2

\frac{9}{16} \\


Option: 3

\frac{11}{16} \\


Option: 4

\frac{13}{16}


Answers (1)

best_answer

The possible relations that are both symmetric and transitive are

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

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

\mathrm{\text { Total number of relations }=2^{2 \cdot 2}=16} \\

\mathrm{\therefore \quad \text { Probability }=\frac{5}{16}}

Hence answer is option 1

Posted by

vishal kumar

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