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CMA Foundation · Fundamentals of Business Mathematics and Statistics · Set Theory, including Venn Diagram

Sets A, B in universal set U satisfy n(A) = 50, n(B) = 40, n(A' ∩ B') = 15 and n(A' ∪ B') = 70. What is n(U)?

The data given are inconsistent, so this question should not be used.

  1. A95
  2. B100Correct
  3. C110
  4. D85

Explanation

n(A' ∪ B') = n(U) − n(A ∩ B) = 70. n(A' ∩ B') = n(U) − n(A ∪ B) = 15. Also n(A ∪ B) = 90 − n(A ∩ B). Let x = n(A ∩ B): n(U) = 70 + x and n(U) = 15 + 90 − x = 105 − x. So 70 + x = 105 − x, x = 17.5, which is not an integer, so the data are inconsistent.

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