Let \(U=\{1,2,3,\ldots,30\}\), \(A=\{x:x\text{ is a multiple of }2\}\), and \(B=\{x:x\text{ is a multiple of }3\}\). What is \(n(A\cap B)\)?
Answer and explanation
Correct answer: 5
The intersection \(A\cap B\) contains numbers that are multiples of both 2 and 3. Such numbers are multiples of \(\operatorname{LCM}(2,3)=6\). Within the universal set from 1 to 30, they are 6, 12, 18, 24, and 30. There are therefore five elements, so \(n(A\cap B)=5\). Option A is correct; the other choices do not count the common multiples accurately.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
The intersection \(A\cap B\) contains numbers that are multiples of both 2 and 3. Such numbers are multiples of \(\operatorname{LCM}(2,3)=6\). Within the universal set from 1 to 30, they are 6, 12, 18, 24, and 30. There are therefore five elements, so \(n(A\cap B)=5\). Option A is correct; the other choices do not count the common multiples accurately.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
