If n(U) = 64, only A has 18 elements, A ∩ B has 12 elements, and only B has 20 elements, how many elements are in the outside region, U − (A ∪ B)?
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Answer and explanation
Correct answer: 14
The universal set is divided into four regions: only A, the intersection A ∩ B, only B, and the region outside both sets. The first three regions contain 18, 12, and 20 elements, so n(A ∪ B) = 18 + 12 + 20 = 50. The outside region therefore contains 64 − 50 = 14 elements. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
14
Why is this the correct answer?
The universal set is divided into four regions: only A, the intersection A ∩ B, only B, and the region outside both sets. The first three regions contain 18, 12, and 20 elements, so n(A ∪ B) = 18 + 12 + 20 = 50. The outside region therefore contains 64 − 50 = 14 elements. Hence option A 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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