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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)} be a relation on A. Which statement about R is correct?

R is symmetric and transitive but not reflexive. The pair (3,3) is absent, so reflexivity fails on A. Each listed pair is its own reverse, giving symmetry, and combining pairs only produces (1,1) or (2,2), which are in R, giving transitivity.

  1. AR is reflexive but not symmetric
  2. BR is symmetric and transitive but not reflexiveCorrect
  3. CR is an equivalence relation on A
  4. DR is symmetric but not transitive

Explanation

(3,3) is missing, so R is not reflexive. Reversing each pair gives the same pair, so R is symmetric. There is no pair (a,b), (b,c) with a different outcome needed, and (1,1),(1,1) gives (1,1), so R is transitive. Hence it is not an equivalence relation, because reflexivity fails on A.

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