In a Venn diagram, n(A ∪ B)=63 and n(A ∩ B)=17. How many elements are in exactly one set?
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Answer and explanation
Correct answer: 46
The union A ∪ B contains elements in A only, B only, and both sets. To retain the elements in exactly one set, remove the common intersection from the union. Thus, n(exactly one)=n(A ∪ B)−n(A ∩ B)=63−17=46. Equivalently, the exactly-one region is (A−B)∪(B−A), so option A is correct.
Frequently asked questions
What is the correct answer to this question?
46
Why is this the correct answer?
The union A ∪ B contains elements in A only, B only, and both sets. To retain the elements in exactly one set, remove the common intersection from the union. Thus, n(exactly one)=n(A ∪ B)−n(A ∩ B)=63−17=46. Equivalently, the exactly-one region is (A−B)∪(B−A), so 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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