If A = {x : x ∈ N, x ≤ 60, 4 divides x} and B = {x : x ∈ N, x ≤ 60, 6 divides x}, what is |A \ B|?
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Answer and explanation
Correct answer: 10
The elements of A are the multiples of 4 from 4 through 60, so |A| = 60/4 = 15. An element belongs to both A and B precisely when it is divisible by both 4 and 6, hence by lcm(4,6) = 12. The multiples of 12 up to 60 are 12, 24, 36, 48, and 60, so |A ∩ B| = 5. Therefore |A \ B| = 15 − 5 = 10.
Frequently asked questions
What is the correct answer to this question?
10
Why is this the correct answer?
The elements of A are the multiples of 4 from 4 through 60, so |A| = 60/4 = 15. An element belongs to both A and B precisely when it is divisible by both 4 and 6, hence by lcm(4,6) = 12. The multiples of 12 up to 60 are 12, 24, 36, 48, and 60, so |A ∩ B| = 5. Therefore |A \ B| = 15 − 5 = 10.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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