CMA Foundation · Fundamentals of Business Mathematics and Statistics · Set Theory, including Venn Diagram
In a universal set U, n(A) = 60, n(B) = 45, and n(A ∪ B) = 85. What is n(A′ ∩ B′) if n(U) = 100?
The value is 15. De Morgan's law shows A′ ∩ B′ equals the complement of A ∪ B, so its size is the universal total minus the union, 100 − 85 = 15. The intersection of 20 is a different quantity and is not asked.
- A15Correct
- B20
- C5
- D40
Explanation
A′ ∩ B′ = (A ∪ B)′ by De Morgan's law. So n = 100 − 85 = 15. The value 20 would come from using n(A ∩ B) = 60+45−85 = 20, which is the intersection, not the complement of the union.
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