In a Venn diagram, only A has 18 elements, only B has 22, only C has 16, only A∩B has 11, only B∩C has 13, only C∩A has 9, and all three have 6 elements. How many elements are in at least two sets?
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Answer and explanation
Correct answer: 39
“At least two sets” includes the three pairwise-only regions and the central region common to all three sets. It therefore excludes the single-set-only regions and includes 11 elements in only A∩B, 13 in only B∩C, 9 in only C∩A, and 6 in A∩B∩C. The total is 11+13+9+6=39. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
39
Why is this the correct answer?
“At least two sets” includes the three pairwise-only regions and the central region common to all three sets. It therefore excludes the single-set-only regions and includes 11 elements in only A∩B, 13 in only B∩C, 9 in only C∩A, and 6 in A∩B∩C. The total is 11+13+9+6=39. Hence 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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