If |U| = 100, |A'| = 58, |B'| = 47, and |A ∩ B| = 21, what is the value of |(A ∪ B)'|?
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Answer and explanation
Correct answer: 26
Since A' contains 58 elements, A contains 100 − 58 = 42 elements. Similarly, B contains 100 − 47 = 53 elements. By inclusion–exclusion, |A ∪ B| = |A| + |B| − |A ∩ B| = 42 + 53 − 21 = 74. Therefore, |(A ∪ B)'| = 100 − 74 = 26. Thus, option C is correct.
Frequently asked questions
What is the correct answer to this question?
26
Why is this the correct answer?
Since A' contains 58 elements, A contains 100 − 58 = 42 elements. Similarly, B contains 100 − 47 = 53 elements. By inclusion–exclusion, |A ∪ B| = |A| + |B| − |A ∩ B| = 42 + 53 − 21 = 74. Therefore, |(A ∪ B)'| = 100 − 74 = 26. Thus, option C is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
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