If A ⊆ U, |U| = 11, and |𝒫(A)| = 128, how many non-empty subsets of A′ are there?
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Answer and explanation
Correct answer: 15
For a finite set X, the power set has 2^|X| members. Since |𝒫(A)| = 128 = 2^7, A has 7 elements. The complement A′ is taken in U, so |A′| = |U| − |A| = 11 − 7 = 4. A four-element set has 2^4 = 16 subsets, including the empty set. Therefore, its non-empty subsets number 16 − 1 = 15, so option B is correct.
Frequently asked questions
What is the correct answer to this question?
15
Why is this the correct answer?
For a finite set X, the power set has 2^|X| members. Since |𝒫(A)| = 128 = 2^7, A has 7 elements. The complement A′ is taken in U, so |A′| = |U| − |A| = 11 − 7 = 4. A four-element set has 2^4 = 16 subsets, including the empty set. Therefore, its non-empty subsets number 16 − 1 = 15, so option B is correct.
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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