If U = {1, 2, ..., 120}, A is the set of multiples of 8 and B is the set of multiples of 12, choose the correct value of n((A ∪ B)').
Answer and explanation
Correct answer: 100
Use the inclusion-exclusion principle. The set A has 15 multiples of 8, while B has 10 multiples of 12. Their overlap consists of multiples of lcm(8, 12) = 24, giving 5 common elements. Therefore n(A ∪ B) = 15 + 10 − 5 = 20. Since the universal set has 120 elements, n((A ∪ B)') = 120 − 20 = 100. Thus option A is unambiguously correct.
Frequently asked questions
What is the correct answer to this question?
100
Why is this the correct answer?
Use the inclusion-exclusion principle. The set A has 15 multiples of 8, while B has 10 multiples of 12. Their overlap consists of multiples of lcm(8, 12) = 24, giving 5 common elements. Therefore n(A ∪ B) = 15 + 10 − 5 = 20. Since the universal set has 120 elements, n((A ∪ B)') = 120 − 20 = 100. Thus option A is unambiguously 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.
