If n(A−B)=38 and n(B−A)=27, what is n(A△B), the cardinality of the symmetric difference?
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Answer and explanation
Correct answer: 65
The symmetric difference A△B contains elements that belong to A or B but not to both. It can be written as (A−B)∪(B−A); these two parts are disjoint. Therefore n(A△B)=n(A−B)+n(B−A)=38+27=65. The common intersection is excluded, so option B is the correct answer.
Frequently asked questions
What is the correct answer to this question?
65
Why is this the correct answer?
The symmetric difference A△B contains elements that belong to A or B but not to both. It can be written as (A−B)∪(B−A); these two parts are disjoint. Therefore n(A△B)=n(A−B)+n(B−A)=38+27=65. The common intersection is excluded, so option B is the correct answer.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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