In a Venn diagram, n(A ∪ B) = 86 and n(A ∩ B) = 31. How many elements belong to exactly one of the two sets?
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Answer and explanation
Correct answer: 55
The union contains every element that is in A, in B, or in both. The elements belonging to exactly one set are the two non-overlapping parts, A − B and B − A. Removing the common part from the union gives their total: 86 − 31 = 55. Therefore, option C is correct; adding the values would count the intersection twice.
Frequently asked questions
What is the correct answer to this question?
55
Why is this the correct answer?
The union contains every element that is in A, in B, or in both. The elements belonging to exactly one set are the two non-overlapping parts, A − B and B − A. Removing the common part from the union gives their total: 86 − 31 = 55. Therefore, option C is correct; adding the values would count the intersection twice.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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