If n(B)=57 and n(A∩B)=23, how many elements are in the only-B region?
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Answer and explanation
Correct answer: 34
The total number of elements in B consists of the elements only in B together with the elements in the intersection A∩B. Hence, n(only B)=n(B)−n(A∩B)=57−23=34. The number 23 is only the common region, and 57 is the entire set B, not just its exclusive part. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
34
Why is this the correct answer?
The total number of elements in B consists of the elements only in B together with the elements in the intersection A∩B. Hence, n(only B)=n(B)−n(A∩B)=57−23=34. The number 23 is only the common region, and 57 is the entire set B, not just its exclusive part. 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).
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