CMA Foundation · Fundamentals of Business Mathematics and Statistics · Set Theory, including Venn Diagram
Let A = {x : x is a natural number, 2 < x ≤ 12 and x is a multiple of 3}. The number of elements in the power set of A is:
The set contains the multiples of 3 in the range, namely 3, 6, 9 and 12, so it has four elements. The power set of a four-element set has 2^4 = 16 elements, so the answer is 16.
- A8
- B16Correct
- C4
- D32
Explanation
Multiples of 3 greater than 2 and at most 12 are 3, 6, 9, 12, so n(A) = 4. The power set has 2^4 = 16 elements. Choosing 8 would result from wrongly counting only 3 elements.
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