Let U = {1, 2, 3, ..., 96}, A be the numbers divisible by 4, and B be the numbers divisible by 6. What is n(A ∪ B)?
Advertisement
Answer and explanation
Correct answer: 32
There are floor(96/4) = 24 multiples of 4 and floor(96/6) = 16 multiples of 6 in U. Numbers counted in both sets are multiples of lcm(4,6) = 12, so there are floor(96/12) = 8 of them. By inclusion-exclusion, n(A ∪ B) = 24 + 16 − 8 = 32. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
32
Why is this the correct answer?
There are floor(96/4) = 24 multiples of 4 and floor(96/6) = 16 multiples of 6 in U. Numbers counted in both sets are multiples of lcm(4,6) = 12, so there are floor(96/12) = 8 of them. By inclusion-exclusion, n(A ∪ B) = 24 + 16 − 8 = 32. Therefore, option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
Advertisement