If n(A−B)=23, n(B−A)=17, and n(A∩B)=12, what is n(A∪B)?
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Answer and explanation
Correct answer: 52
The union A∪B is partitioned into three non-overlapping regions: elements in A but not B, elements in B but not A, and elements common to both A and B. Therefore, n(A∪B)=n(A−B)+n(B−A)+n(A∩B)=23+17+12=52. Each element is counted exactly once in this sum, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
52
Why is this the correct answer?
The union A∪B is partitioned into three non-overlapping regions: elements in A but not B, elements in B but not A, and elements common to both A and B. Therefore, n(A∪B)=n(A−B)+n(B−A)+n(A∩B)=23+17+12=52. Each element is counted exactly once in this sum, so option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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