If A ⊆ U, |A| = 4, and |A'| = 5, what is |P(U)|?
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Answer and explanation
Correct answer: 512
A and its complement A' are disjoint and together form the universal set U. Therefore |U| = |A| + |A'| = 4 + 5 = 9. The power set of an n-element set has 2ⁿ elements, so |P(U)| = 2⁹ = 512. Option B is correct. The other choices are 2⁸, 2¹⁰, and 2¹¹, which use an incorrect size for U.
Frequently asked questions
What is the correct answer to this question?
512
Why is this the correct answer?
A and its complement A' are disjoint and together form the universal set U. Therefore |U| = |A| + |A'| = 4 + 5 = 9. The power set of an n-element set has 2ⁿ elements, so |P(U)| = 2⁹ = 512. Option B is correct. The other choices are 2⁸, 2¹⁰, and 2¹¹, which use an incorrect size for U.
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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