If n(A) = 20 and n(A \ B) = 13, what is n(A ∩ B)?
Answer and explanation
Correct answer: 7
The set A can be divided into two non-overlapping parts: the elements in A \ B and the elements in A ∩ B. Therefore, n(A) = n(A \ B) + n(A ∩ B). Using the given values, 20 = 13 + n(A ∩ B), so n(A ∩ B) = 20 − 13 = 7. Option 13 represents only the difference, while 33 is impossible because it exceeds the total size of A.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
The set A can be divided into two non-overlapping parts: the elements in A \ B and the elements in A ∩ B. Therefore, n(A) = n(A \ B) + n(A ∩ B). Using the given values, 20 = 13 + n(A ∩ B), so n(A ∩ B) = 20 − 13 = 7. Option 13 represents only the difference, while 33 is impossible because it exceeds the total size of 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).
