CMA Foundation · Fundamentals of Business Mathematics and Statistics · Set Theory, including Venn Diagram
A set P has 6 elements. How many subsets of P contain a particular fixed element 'a' of P?
There are 32 such subsets. Once the element 'a' is fixed as a member, each of the remaining 5 elements can either be included or excluded, giving 2^5 = 32 subsets. The figure 64 is the count of all subsets of P, not only those containing 'a'.
- A64
- B16
- C32Correct
- D31
Explanation
Fix 'a' as included. Each of the other 5 elements may be in or out independently, giving 2^5 = 32 subsets. 64 counts all subsets of P, whether or not they contain 'a'. 31 wrongly subtracts one from 32.
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