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

GATE CSE 2020 Q27: Probability that a random relation on {1,2,3} is reflexive

Engineering Mathematics
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Let $\mathcal{R}$ be the set of all binary relations on the set $\{1,2,3\}$ . Suppose a relation is chosen from $\mathcal{R}$ at random. The probability that the chosen relation is reflexive (round off to 3 decimal places) is _______.

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Answer: 0.125 (official GATE 2020 final answer key)

Concept used: A relation is a subset of $A \times A$ ; reflexive relations must contain every pair $(a, a)$ .

First step: There are $2^9$ relations; a reflexive one fixes the 3 diagonal pairs and is free on the other 6, giving $2^6$ .

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Source: official GATE 2020 CS question paper and final answer key, organised by IIT Delhi. Question paper · Answer key

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GATE CSE 2020 Q27: Probability that a random relation on {1,2,3} is reflexive

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