If |U| = 10, |A| = 6, |B| = 5, and |A ∩ B| = 3, what is |P((A ∪ B)′)|?
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Answer and explanation
Correct answer: 4
Use the inclusion–exclusion formula to find the union: |A ∪ B| = |A| + |B| − |A ∩ B| = 6 + 5 − 3 = 8. Since U has 10 elements, the complement of A ∪ B has 10 − 8 = 2 elements. A two-element set has 2² = 4 subsets in its power set. Thus, option B is correct.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
Use the inclusion–exclusion formula to find the union: |A ∪ B| = |A| + |B| − |A ∩ B| = 6 + 5 − 3 = 8. Since U has 10 elements, the complement of A ∪ B has 10 − 8 = 2 elements. A two-element set has 2² = 4 subsets in its power set. Thus, 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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