If n(A ∪ B) = 115 and n(A ∩ B) = 42, what is n(A − B) + n(B − A)?
Answer and explanation
Correct answer: 73
The union consists of three disjoint parts: the elements only in A, the elements only in B, and the common elements in A ∩ B. Therefore, n(A ∪ B) = n(A − B) + n(B − A) + n(A ∩ B). Hence the required value is 115 − 42 = 73. Thus option A is correct. This is also the cardinality of the symmetric difference A △ B.
Frequently asked questions
What is the correct answer to this question?
73
Why is this the correct answer?
The union consists of three disjoint parts: the elements only in A, the elements only in B, and the common elements in A ∩ B. Therefore, n(A ∪ B) = n(A − B) + n(B − A) + n(A ∩ B). Hence the required value is 115 − 42 = 73. Thus option A is correct. This is also the cardinality of the symmetric difference A △ B.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
