If n(A \ B) = 9, n(A ∩ B) = 6, and n(B \ A) = 11, what is n(A ∪ B)?
Answer and explanation
Correct answer: 26
The union is divided into three mutually disjoint regions: elements only in A, elements in both A and B, and elements only in B. Their cardinalities are 9, 6, and 11 respectively. Since these regions together contain every element of A ∪ B, add them: n(A ∪ B) = 9 + 6 + 11 = 26. Therefore option C is correct. Adding only two regions would omit one part of the union.
Frequently asked questions
What is the correct answer to this question?
26
Why is this the correct answer?
The union is divided into three mutually disjoint regions: elements only in A, elements in both A and B, and elements only in B. Their cardinalities are 9, 6, and 11 respectively. Since these regions together contain every element of A ∪ B, add them: n(A ∪ B) = 9 + 6 + 11 = 26. Therefore option C is correct. Adding only two regions would omit one part of the union.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
