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Class 10MathematicsSetsVenn DiagramsMediumLevel 14

If n(A∪B)=58, n(A−B)=22, and n(B−A)=20, which statement is correct?

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Answer and explanation

Correct answer: n(A∩B)=16

The union of two sets is partitioned into three disjoint Venn regions: A−B, B−A, and A∩B. Therefore, n(A∪B) = n(A−B) + n(B−A) + n(A∩B). Substituting the data gives 58 = 22 + 20 + n(A∩B). Thus n(A∩B) = 58−42 = 16. The other choices result from using only one region or subtracting incorrectly, so option A is correct.

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setsVenn diagramsintersectionset differenceMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

n(A∩B)=16

Why is this the correct answer?

The union of two sets is partitioned into three disjoint Venn regions: A−B, B−A, and A∩B. Therefore, n(A∪B) = n(A−B) + n(B−A) + n(A∩B). Substituting the data gives 58 = 22 + 20 + n(A∩B). Thus n(A∩B) = 58−42 = 16. The other choices result from using only one region or subtracting incorrectly, 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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