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CA Foundation · Quantitative Aptitude · Sets, Relations and Functions, Limits and Continuity

Let A = {1, 2, 3} and R = {(1,1), (2,2), (3,3), (1,2), (2,1)} be a relation on A. Which statement about R is correct?

The relation is an equivalence relation. Every element is related to itself, so it is reflexive. Each pair (1,2) has its reverse (2,1), so it is symmetric. Chaining (1,2) and (2,1) gives (1,1) and vice versa gives (2,2), both present, so it is transitive.

  1. AR is reflexive and symmetric but not transitive
  2. BR is an equivalence relationCorrect
  3. CR is symmetric and transitive but not reflexive
  4. DR is reflexive and transitive but not symmetric

Explanation

R contains (1,1), (2,2) and (3,3), so it is reflexive. (1,2) and (2,1) appear together, so it is symmetric. For transitivity, (1,2) and (2,1) force (1,1), and (2,1) and (1,2) force (2,2); both are present. So R is an equivalence relation.

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