n(A − B) = 16 and n(A ∩ B) = 11. What is n(A)?
Answer and explanation
Correct answer: 27
Set A can be divided into two non-overlapping regions: the elements in A but not in B, represented by A − B, and the elements common to both sets, represented by A ∩ B. These two regions together make all of A. Therefore, n(A) = n(A − B) + n(A ∩ B) = 16 + 11 = 27. The overlap is added because it belongs to A.
Frequently asked questions
What is the correct answer to this question?
27
Why is this the correct answer?
Set A can be divided into two non-overlapping regions: the elements in A but not in B, represented by A − B, and the elements common to both sets, represented by A ∩ B. These two regions together make all of A. Therefore, n(A) = n(A − B) + n(A ∩ B) = 16 + 11 = 27. The overlap is added because it belongs to A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
