Let U = {x in N : x <= 60}, A = {multiples of 3 in U}, and B = {multiples of 4 in U}. What is n((A intersection B)')?
Answer and explanation
Correct answer: 55
An element belongs to A intersection B exactly when it is divisible by both 3 and 4. Such numbers are multiples of lcm(3, 4) = 12. From 1 through 60, the multiples are 12, 24, 36, 48, and 60, so the intersection has 5 elements. Since U has 60 elements, its complement has 60 - 5 = 55 elements. Option A is correct.
Frequently asked questions
What is the correct answer to this question?
55
Why is this the correct answer?
An element belongs to A intersection B exactly when it is divisible by both 3 and 4. Such numbers are multiples of lcm(3, 4) = 12. From 1 through 60, the multiples are 12, 24, 36, 48, and 60, so the intersection has 5 elements. Since U has 60 elements, its complement has 60 - 5 = 55 elements. 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.
