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

Let A = {x : x is a natural number, x ≤ 20 and x is a multiple of 3} and B = {x : x is a natural number, x ≤ 20 and x is even}. How many elements does the set A Δ B (symmetric difference, elements in exactly one of A or B) contain?

The symmetric difference has 10 elements. A has 6 elements, B has 10, and their common elements are 6, 12 and 18. Counting those in exactly one set gives 6 + 10 − 2×3 = 10.

  1. A10
  2. B11Correct
  3. C9
  4. D12

Explanation

A = {3,6,9,12,15,18}, so n(A) = 6. B has 10 elements. A ∩ B = multiples of 6 up to 20 = {6,12,18}, so 3 elements. Symmetric difference = 6 + 10 − 2×3 = 10. Check: A only = 3, B only = 7, total 10. The option 11 is wrong; the correct count is 10.

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