If |U| = 15 and |P(A)| = 32, where A ⊆ U, what is |P(A')|?
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Answer and explanation
Correct answer: 2^10
For any finite set X, the number of members in its power set is 2^|X|. Since |P(A)| = 32 = 2^5, A has 5 elements. The complement A' therefore has 15 - 5 = 10 elements because U has 15 elements. Hence |P(A')| = 2^10. Option A is the size of P(A), not P(A'), so option B is the only correct answer.
Frequently asked questions
What is the correct answer to this question?
2^10
Why is this the correct answer?
For any finite set X, the number of members in its power set is 2^|X|. Since |P(A)| = 32 = 2^5, A has 5 elements. The complement A' therefore has 15 - 5 = 10 elements because U has 15 elements. Hence |P(A')| = 2^10. Option A is the size of P(A), not P(A'), so option B is the only correct answer.
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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