If n(P(A)) = 64 and the universal set U has 10 elements, how many elements are in A'?
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Answer and explanation
Correct answer: 4
For a finite set A, the power set contains 2ⁿ(A) subsets. Since n(P(A)) = 64 = 2⁶, A has 6 elements. The complement A' is taken in U, so the complement rule gives n(A') = n(U) − n(A) = 10 − 6 = 4. Thus option A is correct. The value 6 is n(A), not n(A'), and 16 and 32 do not follow from the cardinality rules.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
For a finite set A, the power set contains 2ⁿ(A) subsets. Since n(P(A)) = 64 = 2⁶, A has 6 elements. The complement A' is taken in U, so the complement rule gives n(A') = n(U) − n(A) = 10 − 6 = 4. Thus option A is correct. The value 6 is n(A), not n(A'), and 16 and 32 do not follow from the cardinality rules.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
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