If U={1,2,...,30}, A is the set of multiples of 2, and B is the set of multiples of 5, what is n((A∪B)')?
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Answer and explanation
Correct answer: 12
In U, there are 15 multiples of 2 and 6 multiples of 5. Their overlap consists of multiples of lcm(2,5)=10, namely 10, 20, and 30, so there are 3 common elements. By inclusion-exclusion, n(A∪B)=15+6−3=18. Therefore the complement has n((A∪B)')=30−18=12 elements. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
In U, there are 15 multiples of 2 and 6 multiples of 5. Their overlap consists of multiples of lcm(2,5)=10, namely 10, 20, and 30, so there are 3 common elements. By inclusion-exclusion, n(A∪B)=15+6−3=18. Therefore the complement has n((A∪B)')=30−18=12 elements. Hence option A is correct.
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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