CMA Foundation · Fundamentals of Business Mathematics and Statistics · Set Theory, including Venn Diagram
Which set equals A − (B ∪ C) according to the laws of sets?
A − (B ∪ C) equals (A − B) ∩ (A − C). Rewriting the difference as A ∩ B′ ∩ C′ using De Morgan's law shows an element must be outside both B and C, which is exactly membership in both A − B and A − C.
- A(A − B) ∪ (A − C)
- B(A − B) ∩ (A − C)Correct
- CA′ ∩ (B ∪ C)
- D(A ∩ B) − C
Explanation
A − (B ∪ C) = A ∩ (B ∪ C)′ = A ∩ B′ ∩ C′ by De Morgan. This equals (A ∩ B′) ∩ (A ∩ C′) = (A − B) ∩ (A − C). The union version includes elements removed by only one of B or C, so it is larger.
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