CMA Foundation · Fundamentals of Business Mathematics and Statistics · Set Theory, including Venn Diagram
Let the universal set U = {1, 2, 3, ..., 12}, A = {2, 4, 6, 8, 10, 12} and B = {3, 6, 9, 12}. What is the number of elements in (A ∪ B)′, the complement of A ∪ B?
The union of A and B contains 8 elements, namely 2, 3, 4, 6, 8, 9, 10 and 12. The universal set has 12 elements, so the complement has 12 minus 8, which is 4 elements: 1, 5, 7 and 11.
- A4
- B5Correct
- C6
- D7
Explanation
A ∪ B = {2, 3, 4, 6, 8, 9, 10, 12}, which has 8 elements. The complement has 12 − 8 = 4 elements: {1, 5, 7, 11}. Wait, the count of elements outside is 4, so option 4 is right; the distractor 8 would be counting A ∪ B itself.
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