If U = {1, 2, ..., 70}, A = {x : x is divisible by 5}, and B = {x : x is divisible by 7}, what is |A' ∩ B|?
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Answer and explanation
Correct answer: 8
A' ∩ B consists of elements that are divisible by 7 but not divisible by 5. From 1 to 70, B contains 70/7 = 10 numbers. The numbers divisible by both 5 and 7 are multiples of lcm(5, 7) = 35, namely 35 and 70, so there are 2 such numbers. Therefore, |A' ∩ B| = 10 − 2 = 8, making option C correct.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
A' ∩ B consists of elements that are divisible by 7 but not divisible by 5. From 1 to 70, B contains 70/7 = 10 numbers. The numbers divisible by both 5 and 7 are multiples of lcm(5, 7) = 35, namely 35 and 70, so there are 2 such numbers. Therefore, |A' ∩ B| = 10 − 2 = 8, making option C 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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