GATE Computer Science (CS) 2020 Solved Papers

Question : 22 of 65

Marks: +1, -0

Let R be the set of all binary relations on the se {1. 2, 3}. Suppose a relation chosen from R at random. The probability that the chosen relation is reflex (round off to 3 decimal places) is ________.

Your Answer:

Validate

Solution:

No. of relation on

{A}=2^{9}

No. of reflexive relation on

{A}=2^{∧}( {n}^{2}- {n})=2^{∧}(3^{2}-3)=2^{6}

∴

Probability (reflexive)

=\;{2^{6}}/{2^{9}}=\;{1}/{8}=0.125

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