If U = {1, 2, …, 36}, A = {x : x is divisible by 2}, and B = {x : x is divisible by 3}, what is |A′ ∩ B′|?
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Answer and explanation
Correct answer: 12
By De Morgan’s law, A′ ∩ B′ = (A ∪ B)′. Among the numbers 1 to 36, 18 are divisible by 2, 12 are divisible by 3, and 6 are divisible by both because they are multiples of 6. Hence |A ∪ B| = 18 + 12 − 6 = 24. Its complement in U therefore has 36 − 24 = 12 elements, so option C is correct.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
By De Morgan’s law, A′ ∩ B′ = (A ∪ B)′. Among the numbers 1 to 36, 18 are divisible by 2, 12 are divisible by 3, and 6 are divisible by both because they are multiples of 6. Hence |A ∪ B| = 18 + 12 − 6 = 24. Its complement in U therefore has 36 − 24 = 12 elements, so 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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