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 …

Official answer: 0.125. Explanation: Let A = \1, 2, 3\. The number of elements in A is n = 3. 1. The total number of pairs in A A is n2 = 32 = 9. 2. The total number of binary relations on A is: | R| = 2n2 = 29 = 512 3. For a relation to be reflexive, it must contain all n = 3 diagonal pairs (1, 1), (2, 2), (3, 3). The remaining n2 - n = 9 - 3 = 6 non-diagonal pairs can either be present or absent independently. 4. Thus, the number of reflexive relations is: 2n(n-1) = 29-3 = 26 = 64 5. The probability of choosing a reflexive relation at random is: P = 2629 = 123 = 18 = 0.125 Rounded to 3 decimal places, the answer is 0.125.

Engineering Mathematics · Discrete Mathematics

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GATE CSE 2020 Q17 · NAT · 1 mark

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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Discrete Mathematics

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In GATE Computer Science, Discrete Mathematics is heavily tested across mathematical logic, set theory, relations & partial orders/lattices, group theory, combinatorics, and graph theory. Questions evaluate formal reasoning, counterexample construction, and structural counting principles. Over recent years, question formats have transitioned from standard single-choice definitions to multi-select properties (MSQs) and exact integer/combinatorial numerical answers (NATs).

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Engineering Mathematics · Discrete Mathematics

Official IIT answer key · IIT Delhi · Audited Aug 2026

Take topic test

GATE CSE 2020 Q17 · NAT · 1 mark

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 ________.

Numerical answer

Enter a value to check

Key concept

Discrete Mathematics

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Examiner trap & misconception

Topic notes

How GATE tests Discrete Mathematics

Full Discrete Mathematics guide →

More on Discrete Mathematics

All 50 questions on Discrete Mathematics →

Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.

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

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

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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 ________.

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 ________.