CMA Foundation · Fundamentals of Business Mathematics and Statistics · Set Theory, including Venn Diagram
A set P has 5 elements. How many subsets of P have at least one element and are not equal to P itself (non-empty proper subsets)?
There are 30 non-empty proper subsets. A set of 5 elements has 2^5, or 32, subsets in all. Excluding the empty subset and the set itself removes 2, leaving 30.
- A32
- B30Correct
- C31
- D25
Explanation
Total subsets are 2^5 = 32. Removing the empty set and P itself leaves 32 − 2 = 30. The option 31 only removes the empty set, so it still counts P.
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