In a survey there are 45 people in set A, 50 in B, and 42 in C; n(A ∩ B)=18, n(B ∩ C)=20, n(C ∩ A)=16, and 7 people are in all three. How many people are only in A?
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Answer and explanation
Correct answer: 18
The pairwise intersections include the seven people who belong to all three sets. Thus the A∩B-only region is 18−7=11, and the C∩A-only region is 16−7=9. Set A contains its A-only region, these two pairwise-only regions, and the triple region. Hence A-only=45−11−9−7=18. Therefore option A is correct.
Frequently asked questions
What is the correct answer to this question?
18
Why is this the correct answer?
The pairwise intersections include the seven people who belong to all three sets. Thus the A∩B-only region is 18−7=11, and the C∩A-only region is 16−7=9. Set A contains its A-only region, these two pairwise-only regions, and the triple region. Hence A-only=45−11−9−7=18. 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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