If \(A=\{x\in\mathbb{N}:x\le30,\ 2\mid x\}\) and \(B=\{x\in\mathbb{N}:x\le30,\ 3\mid x\}\), what is \(A\cap B\)?
Answer and explanation
Correct answer: \(\{6,12,18,24,30\}\)
An element belongs to \(A\cap B\) only if it is divisible by both 2 and 3 and is at most 30. Every number divisible by both 2 and 3 is divisible by their least common multiple, \(\operatorname{lcm}(2,3)=6\). The positive multiples of 6 not exceeding 30 are \(6,12,18,24,30\). Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
\(\{6,12,18,24,30\}\)
Why is this the correct answer?
An element belongs to \(A\cap B\) only if it is divisible by both 2 and 3 and is at most 30. Every number divisible by both 2 and 3 is divisible by their least common multiple, \(\operatorname{lcm}(2,3)=6\). The positive multiples of 6 not exceeding 30 are \(6,12,18,24,30\). Hence 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).
