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Subjects
Class 10MathematicsSetsVenn DiagramsHardLevel 11

If n(A ∪ B ∪ C) = 140, exactly one set has 65 elements and exactly two sets have 51 elements, what is n(A ∩ B ∩ C)?

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Answer and explanation

Correct answer: 24

The union is partitioned into three mutually exclusive types of Venn regions: elements belonging to exactly one set, elements belonging to exactly two sets, and elements belonging to all three sets. Thus 140 = 65 + 51 + n(A ∩ B ∩ C). Solving gives n(A ∩ B ∩ C) = 140 − 116 = 24. Therefore option A is correct.

Tags

setsVenn diagramsexactly two setstriple intersectionMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

24

Why is this the correct answer?

The union is partitioned into three mutually exclusive types of Venn regions: elements belonging to exactly one set, elements belonging to exactly two sets, and elements belonging to all three sets. Thus 140 = 65 + 51 + n(A ∩ B ∩ C). Solving gives n(A ∩ B ∩ C) = 140 − 116 = 24. Therefore 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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