If \(U=\{1,2,\ldots,30\}\), \(A=\{x:x\in U,\ 2\mid x\}\) and \(B=\{x:x\in U,\ 3\mid x\}\), what is \(n(A\cup B)\)?
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Answer and explanation
Correct answer: 20
The set A contains the 15 multiples of 2 from 1 to 30, and B contains the 10 multiples of 3. Numbers counted in both sets are multiples of 6; there are 5 of them: 6, 12, 18, 24, and 30. Therefore, inclusion–exclusion gives \(n(A\cup B)=n(A)+n(B)-n(A\cap B)=15+10-5=20\).
Frequently asked questions
What is the correct answer to this question?
20
Why is this the correct answer?
The set A contains the 15 multiples of 2 from 1 to 30, and B contains the 10 multiples of 3. Numbers counted in both sets are multiples of 6; there are 5 of them: 6, 12, 18, 24, and 30. Therefore, inclusion–exclusion gives \(n(A\cup B)=n(A)+n(B)-n(A\cap B)=15+10-5=20\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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