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Class 10MathematicsSetsVenn DiagramsHardLevel 14

For three sets, n(A) = 90, n(B) = 84, n(C) = 78, n(A ∩ B) = 36, n(B ∩ C) = 32, n(C ∩ A) = 30, and n(A ∩ B ∩ C) = 13. What is n(A ∪ B ∪ C)?

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Answer and explanation

Correct answer: 167

Apply the inclusion-exclusion formula for three sets: n(A ∪ B ∪ C) = n(A) + n(B) + n(C) − n(A ∩ B) − n(B ∩ C) − n(C ∩ A) + n(A ∩ B ∩ C). Substitution gives 90 + 84 + 78 − 36 − 32 − 30 + 13 = 167. The triple intersection is added once at the end because it was subtracted too many times. Thus option B is correct.

Tags

setsinclusion-exclusionthree-set unionVenn diagramsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

167

Why is this the correct answer?

Apply the inclusion-exclusion formula for three sets: n(A ∪ B ∪ C) = n(A) + n(B) + n(C) − n(A ∩ B) − n(B ∩ C) − n(C ∩ A) + n(A ∩ B ∩ C). Substitution gives 90 + 84 + 78 − 36 − 32 − 30 + 13 = 167. The triple intersection is added once at the end because it was subtracted too many times. Thus option B 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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