Let \(U=\{1,2,\ldots,50\}\), \(A=\{x:x\in U,\ 4\mid x\}\), and \(B=\{x:x\in U,\ 6\mid x\}\). What is \(n(A\cap B)\)?
Answer and explanation
Correct answer: 4
An element belongs to \(A\cap B\) only when it is divisible by both 4 and 6. Such numbers are multiples of their least common multiple: \(\operatorname{lcm}(4,6)=12\). The multiples of 12 from 1 through 50 are \(12,24,36,48\). There are four such elements, so \(n(A\cap B)=4\). Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
An element belongs to \(A\cap B\) only when it is divisible by both 4 and 6. Such numbers are multiples of their least common multiple: \(\operatorname{lcm}(4,6)=12\). The multiples of 12 from 1 through 50 are \(12,24,36,48\). There are four such elements, so \(n(A\cap B)=4\). Therefore, 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).
