If n(A ∪ B ∪ C) = 180, n(A ∩ B ∩ C) = 20, and 70 elements lie in exactly two of the sets, how many elements lie in exactly one set?
Answer and explanation
Correct answer: 90
For three sets, the union can be divided into disjoint regions: elements in exactly one set, elements in exactly two sets, and elements in all three sets. Hence, n(A ∪ B ∪ C) = exactly-one + exactly-two + exactly-three. Substitution gives 180 = exactly-one + 70 + 20, so exactly-one = 180 − 90 = 90. Therefore, option B is correct.
Frequently asked questions
What is the correct answer to this question?
90
Why is this the correct answer?
For three sets, the union can be divided into disjoint regions: elements in exactly one set, elements in exactly two sets, and elements in all three sets. Hence, n(A ∪ B ∪ C) = exactly-one + exactly-two + exactly-three. Substitution gives 180 = exactly-one + 70 + 20, so exactly-one = 180 − 90 = 90. Therefore, option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
