Let U = {1, 2, ..., 30}. If A is the set of multiples of 2 in U and B is the set of multiples of 5 in U, what is n(A ∪ B)?
Answer and explanation
Correct answer: 18
Use the inclusion–exclusion principle, because multiples common to A and B would otherwise be counted twice. There are floor(30/2) = 15 multiples of 2 and floor(30/5) = 6 multiples of 5. The overlap consists of multiples of lcm(2,5) = 10, namely 10, 20, and 30, so it has 3 elements. Therefore n(A ∪ B) = 15 + 6 − 3 = 18. Option A is correct; adding without subtraction gives the distractor 21.
Frequently asked questions
What is the correct answer to this question?
18
Why is this the correct answer?
Use the inclusion–exclusion principle, because multiples common to A and B would otherwise be counted twice. There are floor(30/2) = 15 multiples of 2 and floor(30/5) = 6 multiples of 5. The overlap consists of multiples of lcm(2,5) = 10, namely 10, 20, and 30, so it has 3 elements. Therefore n(A ∪ B) = 15 + 6 − 3 = 18. Option A is correct; adding without subtraction gives the distractor 21.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
