If n(A∪B∪C)=156, 74 elements are in exactly one set, and 17 elements are in all three sets, how many elements are in exactly two sets?
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Answer and explanation
Correct answer: 65
The union of three sets can be partitioned into three mutually exclusive categories: elements in exactly one set, elements in exactly two sets, and elements in all three sets. Let x be the number in exactly two sets. Then 156 = 74 + x + 17. Hence x = 156 − 74 − 17 = 65. Thus, 65 elements lie in exactly two of the three sets.
Frequently asked questions
What is the correct answer to this question?
65
Why is this the correct answer?
The union of three sets can be partitioned into three mutually exclusive categories: elements in exactly one set, elements in exactly two sets, and elements in all three sets. Let x be the number in exactly two sets. Then 156 = 74 + x + 17. Hence x = 156 − 74 − 17 = 65. Thus, 65 elements lie in exactly two of the three sets.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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