The number of elements in the power set of A ∪ B, where A = {2, 3, 5, 7} and B…
2012
The number of elements in the power set of A ∪ B, where A = {2, 3, 5, 7} and B = {2, 5, 8, 9}, is
Answer: B. 64 — ConceptFor any finite set S with n distinct elements, its power set P(S) contains every possible subset of S. Each element has two independent choices—either…
- A.
256
- B.
64
- C.
16
- D.
4
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Correct answer: B
Concept
For any finite set S with n distinct elements, its power set P(S) contains every possible subset of S. Each element has two independent choices—either included or excluded—so |P(S)| = 2n.
Application
Form the union by listing each distinct element only once: A ∪ B = {2, 3, 5, 7, 8, 9}.
Thus |A ∪ B| = 6.
Therefore |P(A ∪ B)| = 26 = 64.
Cross-check
A four-element set has 16 subsets. Adding the two new elements 8 and 9 doubles the subset count twice: 16 × 2 × 2 = 64.
Hence, the power set of A ∪ B has 64 elements.