Let N = {1, 2, 3, ...}. If A = {x ∈ N : x ≤ 50 and 4 divides x} and B = {x ∈ N : x ≤ 50 and 6 divides x}, what is n(A ∩ B)?
Answer and explanation
Correct answer: 4
A number belongs to A ∩ B precisely when it is divisible by both 4 and 6. Such numbers are multiples of lcm(4, 6) = 12. The positive multiples of 12 not exceeding 50 are 12, 24, 36, and 48. There are four numbers, so n(A ∩ B) = 4. The definition of N as positive natural numbers removes any ambiguity about including zero.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
A number belongs to A ∩ B precisely when it is divisible by both 4 and 6. Such numbers are multiples of lcm(4, 6) = 12. The positive multiples of 12 not exceeding 50 are 12, 24, 36, and 48. There are four numbers, so n(A ∩ B) = 4. The definition of N as positive natural numbers removes any ambiguity about including zero.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
