If U = {1, 2, …, 60}, A = {x ∈ U : 2 divides x}, and B = {x ∈ U : 3 divides x}, what is |A ∪ B|?
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Answer and explanation
Correct answer: 40
There are floor(60/2) = 30 multiples of 2 and floor(60/3) = 20 multiples of 3 in U. Elements divisible by both 2 and 3 are multiples of 6, and there are floor(60/6) = 10 of them. By inclusion–exclusion, |A ∪ B| = |A| + |B| − |A ∩ B| = 30 + 20 − 10 = 40.
Frequently asked questions
What is the correct answer to this question?
40
Why is this the correct answer?
There are floor(60/2) = 30 multiples of 2 and floor(60/3) = 20 multiples of 3 in U. Elements divisible by both 2 and 3 are multiples of 6, and there are floor(60/6) = 10 of them. By inclusion–exclusion, |A ∪ B| = |A| + |B| − |A ∩ B| = 30 + 20 − 10 = 40.
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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