If U = {1, 2, ..., 40}, A is the set of multiples of 5, and B is the set of multiples of 8, what is n((A ∩ B)′)?
Answer and explanation
Correct answer: 39
An element in A ∩ B must be divisible by both 5 and 8, so it must be a multiple of lcm(5,8) = 40. Within U = {1,2,...,40}, the only such element is 40 itself. Therefore n(A ∩ B) = 1. The universal set has 40 elements, so the complement contains 40 − 1 = 39 elements. Hence n((A ∩ B)′) = 39 and option A is correct.
Frequently asked questions
What is the correct answer to this question?
39
Why is this the correct answer?
An element in A ∩ B must be divisible by both 5 and 8, so it must be a multiple of lcm(5,8) = 40. Within U = {1,2,...,40}, the only such element is 40 itself. Therefore n(A ∩ B) = 1. The universal set has 40 elements, so the complement contains 40 − 1 = 39 elements. Hence n((A ∩ B)′) = 39 and option A is 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.
