CMA Foundation · Fundamentals of Business Mathematics and Statistics · Set Theory, including Venn Diagram
For sets A and B in a universal set U, n(U) = 120, n(A ∩ B) = 25 and n(A ∪ B) = 90. What is n(A' ∪ B')?
The answer is 95. By De Morgan's law, the union of the complements equals the complement of the intersection. Therefore n(A' ∪ B') = n(U) − n(A ∩ B) = 120 − 25 = 95. The union figure of 90 is not needed here.
- A30
- B95Correct
- C65
- D25
Explanation
De Morgan: A' ∪ B' = (A ∩ B)'. So n(A' ∪ B') = n(U) − n(A ∩ B) = 120 − 25 = 95. The value 30 is n(A ∪ B)' which equals (A' ∩ B'), a different set; 65 is 90 − 25, which is the number in exactly one set.
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