GATE 2020 CS – Question 27

Engineering Mathematics · Discrete Mathematics: Sets, Relations, Functions, Partial Orders and Lattices · 1 mark · Numerical answer

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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Correct answer: 0.125 to 0.125

Explanation

There are $2^9=512$ relations. Reflexive ones must contain the 3 diagonal pairs, leaving $2^6=64$ choices. Probability = 64/512 = 0.125.