If only A has 21 elements, only B has 24, only C has 18, only A∩B has 13, only B∩C has 11, only C∩A has 9, and all three sets have 7 elements, how many elements belong to exactly two sets?
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Answer and explanation
Correct answer: 33
The phrase “exactly two sets” refers only to the three pairwise-only regions: A∩B excluding C, B∩C excluding A, and C∩A excluding B. Therefore, add 13, 11, and 9: 13+11+9=33. The central region containing all three sets is not included because those elements belong to three sets, not exactly two.
Frequently asked questions
What is the correct answer to this question?
33
Why is this the correct answer?
The phrase “exactly two sets” refers only to the three pairwise-only regions: A∩B excluding C, B∩C excluding A, and C∩A excluding B. Therefore, add 13, 11, and 9: 13+11+9=33. The central region containing all three sets is not included because those elements belong to three sets, not exactly two.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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