If \(A=\{x\in\mathbb{N}:x\mid18\}\) and \(B=\{x\in\mathbb{N}:x\mid24\}\), what is \(A\cup B\)?
Answer and explanation
Correct answer: \(\{1,2,3,4,6,8,9,12,18,24\}\)
The positive divisors of 18 are \(\{1,2,3,6,9,18\}\), and the positive divisors of 24 are \(\{1,2,3,4,6,8,12,24\}\). A union contains every element belonging to at least one set, with repeated elements written only once. Combining these lists gives \(\{1,2,3,4,6,8,9,12,18,24\}\), so option A is correct.
Frequently asked questions
What is the correct answer to this question?
\(\{1,2,3,4,6,8,9,12,18,24\}\)
Why is this the correct answer?
The positive divisors of 18 are \(\{1,2,3,6,9,18\}\), and the positive divisors of 24 are \(\{1,2,3,4,6,8,12,24\}\). A union contains every element belonging to at least one set, with repeated elements written only once. Combining these lists gives \(\{1,2,3,4,6,8,9,12,18,24\}\), so option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
