CMA Foundation · Fundamentals of Business Mathematics and Statistics · Set Theory, including Venn Diagram
A set A has 5 elements. How many subsets of A are proper subsets?
A set with five elements has 2^5 = 32 subsets in all. Proper subsets exclude the set itself, so the number of proper subsets is 32 minus 1, which equals 31. The figure 32 wrongly includes the set itself.
- A31Correct
- B32
- C25
- D10
Explanation
A set with n elements has 2^n subsets. Here 2^5 = 32. A proper subset excludes the set itself, so proper subsets = 32 - 1 = 31. The value 32 counts A itself as a subset, so it is wrong.
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