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

Let A = {1, 2, 3} and R = {(1,2), (2,3), (1,3)} be a relation on A. What is the minimum number of ordered pairs that must be added to R to make it both reflexive and symmetric?

The minimum number of pairs to add is 6. Reflexivity requires the three pairs (1,1), (2,2), (3,3), and symmetry requires the three reverses (2,1), (3,2), (3,1). These sets are disjoint and none are already in R, giving 3 + 3 = 6.

  1. A3
  2. B6Correct
  3. C5
  4. D8

Explanation

Reflexive needs (1,1), (2,2), (3,3): 3 pairs. Symmetric needs reverses (2,1), (3,2), (3,1): 3 pairs, none already present and none overlapping with the diagonal ones. Total 3 + 3 = 6. The option 3 counts only one requirement.

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