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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), (1, 2), (2, 3)} be a relation on A. Which of the following ordered pairs must be added to R, at minimum, to make R reflexive?

Only (3, 3) must be added. A reflexive relation on {1, 2, 3} needs (1,1), (2,2) and (3,3). The first two are already present, so the sole missing pair is (3,3). Other pairs relate to symmetry or transitivity, not reflexivity.

  1. A(3, 3) onlyCorrect
  2. B(3, 3) and (2, 1)
  3. C(3, 3) and (1, 3)
  4. D(1, 2) and (3, 3)

Explanation

A reflexive relation on A must contain (1,1), (2,2) and (3,3). R already has (1,1) and (2,2), so only (3,3) is missing. Adding (2,1) or (1,3) concerns symmetry or transitivity, not reflexivity, and (1,2) is already in R.

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