If n(A)=20, n(B)=24 and only A has 13 elements, that is, n(A\B)=13, what is n(A∩B)?
Answer and explanation
Correct answer: 7
Set A is divided into two non-overlapping parts: the elements only in A, represented by A\B, and the elements common to A and B, represented by A∩B. Hence n(A)=n(A\B)+n(A∩B). Substituting the given values gives 20=13+n(A∩B), so n(A∩B)=20−13=7. Thus option A is correct; 13 is the exclusive part, not the common part.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
Set A is divided into two non-overlapping parts: the elements only in A, represented by A\B, and the elements common to A and B, represented by A∩B. Hence n(A)=n(A\B)+n(A∩B). Substituting the given values gives 20=13+n(A∩B), so n(A∩B)=20−13=7. Thus option A is correct; 13 is the exclusive part, not the common part.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
