If n(A) = 21, the number of elements only in A is 13, that is, n(A \ B) = 13, and n(B \ A) = 10, what is n(A ∪ B)?
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Answer and explanation
Correct answer: 31
The set A is divided into its A-only part and its common part. Hence n(A ∩ B) = n(A) − n(A \ B) = 21 − 13 = 8. The union contains three disjoint parts: A \ B, A ∩ B, and B \ A. Therefore, n(A ∪ B) = 13 + 8 + 10 = 31. Option B is correct; 23 omits the common part, while 34 and 44 use unsuitable totals.
Frequently asked questions
What is the correct answer to this question?
31
Why is this the correct answer?
The set A is divided into its A-only part and its common part. Hence n(A ∩ B) = n(A) − n(A \ B) = 21 − 13 = 8. The union contains three disjoint parts: A \ B, A ∩ B, and B \ A. Therefore, n(A ∪ B) = 13 + 8 + 10 = 31. Option B is correct; 23 omits the common part, while 34 and 44 use unsuitable totals.
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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