If n(A ∩ B) = 48, n(A ∩ C) = 41, n(B ∩ C) = 39, and n(A ∩ B ∩ C) = 17, how many elements belong to at least two sets?
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Answer and explanation
Correct answer: 94
First find the elements in exactly two sets by removing the triple intersection from each pair: (48 − 17) + (41 − 17) + (39 − 17) = 31 + 24 + 22 = 77. The elements in all three sets, 17, must then be included because “at least two” means exactly two or exactly three. Thus the required number is 77 + 17 = 94, option B.
Frequently asked questions
What is the correct answer to this question?
94
Why is this the correct answer?
First find the elements in exactly two sets by removing the triple intersection from each pair: (48 − 17) + (41 − 17) + (39 − 17) = 31 + 24 + 22 = 77. The elements in all three sets, 17, must then be included because “at least two” means exactly two or exactly three. Thus the required number is 77 + 17 = 94, option B.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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