If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 2, 3, 4}, and B = {3, 4, 5, 6}, how many elements are in (A ∩ B)′?
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Answer and explanation
Correct answer: 8
The intersection consists of elements common to both sets. Thus, A ∩ B = {3, 4}, which has 2 elements. The complement is taken in U, which has 10 elements. Therefore, n((A ∩ B)′) = n(U) − n(A ∩ B) = 10 − 2 = 8. Hence option A is correct; the value 2 is the size of the intersection itself, not its complement.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The intersection consists of elements common to both sets. Thus, A ∩ B = {3, 4}, which has 2 elements. The complement is taken in U, which has 10 elements. Therefore, n((A ∩ B)′) = n(U) − n(A ∩ B) = 10 − 2 = 8. Hence option A is correct; the value 2 is the size of the intersection itself, not its complement.
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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