If O₁ = {x : x ∈ ℕ, x ≤ 50, and x is divisible by both 4 and 6}, what is the roster form of O₁?
Answer and explanation
Correct answer: O₁ = {12, 24, 36, 48}
A number divisible by both 4 and 6 must be divisible by their least common multiple. Since lcm(4, 6) = 12, the required numbers are multiples of 12. The positive multiples of 12 that are at most 50 are 12, 24, 36 and 48. Thus, the roster form is O₁ = {12, 24, 36, 48}. Numbers such as 4 or 6 satisfy only one of the two divisibility conditions.
Frequently asked questions
What is the correct answer to this question?
O₁ = {12, 24, 36, 48}
Why is this the correct answer?
A number divisible by both 4 and 6 must be divisible by their least common multiple. Since lcm(4, 6) = 12, the required numbers are multiples of 12. The positive multiples of 12 that are at most 50 are 12, 24, 36 and 48. Thus, the roster form is O₁ = {12, 24, 36, 48}. Numbers such as 4 or 6 satisfy only one of the two divisibility conditions.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
