If A \ B has 5 elements, B \ A has 7 elements, and A ∩ B has 4 elements, what is n(A ∪ B)?
Answer and explanation
Correct answer: 16
The union A ∪ B is divided into three mutually disjoint regions: elements belonging only to A, represented by A \ B; elements belonging only to B, represented by B \ A; and elements common to both, represented by A ∩ B. Therefore no element is counted twice when these three numbers are added: n(A ∪ B) = 5 + 7 + 4 = 16.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
The union A ∪ B is divided into three mutually disjoint regions: elements belonging only to A, represented by A \ B; elements belonging only to B, represented by B \ A; and elements common to both, represented by A ∩ B. Therefore no element is counted twice when these three numbers are added: n(A ∪ B) = 5 + 7 + 4 = 16.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
