If n(A−B)=23 and n(B−A)=31, what is n(A △ B)?
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Answer and explanation
Correct answer: 54
The symmetric difference A △ B is the union of the two disjoint regions A−B and B−A. These regions cannot contain the same element, because the first excludes B and the second excludes A. Therefore, their cardinalities are added: n(A △ B)=n(A−B)+n(B−A)=23+31=54. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
54
Why is this the correct answer?
The symmetric difference A △ B is the union of the two disjoint regions A−B and B−A. These regions cannot contain the same element, because the first excludes B and the second excludes A. Therefore, their cardinalities are added: n(A △ B)=n(A−B)+n(B−A)=23+31=54. Hence 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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