If A ⊆ U, |U| = 7, and |P(A′)| = 8, what is |A|?
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Answer and explanation
Correct answer: 4
For any finite set X, the number of members in its power set is |P(X)| = 2^|X|. Here, |P(A′)| = 8 = 2^3, so |A′| = 3. Since A and A′ partition the universal set U, their cardinalities add to |U|: |A| + |A′| = 7. Therefore, |A| = 7 − 3 = 4, making option C the only correct answer.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
For any finite set X, the number of members in its power set is |P(X)| = 2^|X|. Here, |P(A′)| = 8 = 2^3, so |A′| = 3. Since A and A′ partition the universal set U, their cardinalities add to |U|: |A| + |A′| = 7. Therefore, |A| = 7 − 3 = 4, making option C 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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