If \(n(B)=41\) and \(n(A\cap B)=17\), how many elements are only in \(B\)?
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Answer and explanation
Correct answer: 24
The elements of B consist of two non-overlapping groups: those only in B and those in the intersection \(A\cap B\). Therefore, \(n(B-A)=n(B)-n(A\cap B)=41-17=24\). Option B is correct. The number 17 counts only the shared elements, and 41 counts the whole of B, so neither represents the only-B region.
Frequently asked questions
What is the correct answer to this question?
24
Why is this the correct answer?
The elements of B consist of two non-overlapping groups: those only in B and those in the intersection \(A\cap B\). Therefore, \(n(B-A)=n(B)-n(A\cap B)=41-17=24\). Option B is correct. The number 17 counts only the shared elements, and 41 counts the whole of B, so neither represents the only-B region.
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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