If U = {1, 2, ..., 15}, A = {1, 4, 9}, and B = {2, 4, 6, 8, 10, 12, 14}, how many elements are in (A ∩ B)′?
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Answer and explanation
Correct answer: 14
First find the intersection of A and B. The only common element is 4, so A ∩ B = {4} and |A ∩ B| = 1. The complement is taken with respect to U, which contains 15 elements. Therefore, |(A ∩ B)′| = |U| − |A ∩ B| = 15 − 1 = 14. Hence, option B is correct.
Frequently asked questions
What is the correct answer to this question?
14
Why is this the correct answer?
First find the intersection of A and B. The only common element is 4, so A ∩ B = {4} and |A ∩ B| = 1. The complement is taken with respect to U, which contains 15 elements. Therefore, |(A ∩ B)′| = |U| − |A ∩ B| = 15 − 1 = 14. Hence, option B 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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