CMA Foundation · Fundamentals of Business Mathematics and Statistics · Set Theory, including Venn Diagram
If A = {1, 2, 3, 4} and B = {1, 2, 3, 4, 5, 6}, how many subsets of B contain all elements of A?
Each such subset must contain the four elements of A, leaving only 5 and 6 free to be included or not. That gives 2 × 2 = 4 subsets. The figure 16 wrongly treats the elements of A as optional.
- A2
- B4Correct
- C8
- D16
Explanation
Any subset containing all of A must include 1, 2, 3, 4. The remaining elements 5 and 6 may each be included or excluded freely, giving 2^2 = 4 subsets. The value 16 is 2^4, which wrongly counts free choices over A's elements.
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