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

A relation R is defined on A = {1, 2, 3, 4, 5, 6} by R = {(a, b) : a − b is even}. How many ordered pairs does R contain?

R contains 18 ordered pairs. The difference is even only when both numbers have the same parity. The three odd numbers form 3 × 3 = 9 pairs and the three even numbers form another 9 pairs, so the total is 18.

  1. A18Correct
  2. B36
  3. C12
  4. D24

Explanation

a − b is even when both are odd or both are even. Odd elements: 1, 3, 5 give 3 × 3 = 9 pairs. Even elements: 2, 4, 6 give 3 × 3 = 9 pairs. Total 18. The option 36 is the whole A × A, ignoring the condition.

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