If |U| = 90, |A ∩ B| = 24, |A′ ∩ B| = 17, and |A′ ∩ B′| = 29, what is |A ∩ B′|?
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Answer and explanation
Correct answer: 20
The universal set is partitioned into four mutually disjoint regions: A ∩ B, A′ ∩ B, A′ ∩ B′, and A ∩ B′. Their cardinalities must add to |U|. Therefore |A ∩ B′| = 90 − 24 − 17 − 29 = 20. Hence option B is correct. This partition prevents any element from being counted twice or omitted.
Frequently asked questions
What is the correct answer to this question?
20
Why is this the correct answer?
The universal set is partitioned into four mutually disjoint regions: A ∩ B, A′ ∩ B, A′ ∩ B′, and A ∩ B′. Their cardinalities must add to |U|. Therefore |A ∩ B′| = 90 − 24 − 17 − 29 = 20. Hence option B is correct. This partition prevents any element from being counted twice or omitted.
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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