If n(A − B) = 32 and n(A intersection B) = 18, what is n(A)?
Answer and explanation
Correct answer: 50
The set A can be divided into two non-overlapping regions: A − B, containing elements that are in A but not in B, and A intersection B, containing elements common to both sets. Their union is A, so their cardinalities add. Thus n(A) = n(A − B) + n(A intersection B) = 32 + 18 = 50. Subtracting the values would be incorrect because the two given regions are separate parts of A, not quantities to be removed from one another. Therefore, option B is correct.
Frequently asked questions
What is the correct answer to this question?
50
Why is this the correct answer?
The set A can be divided into two non-overlapping regions: A − B, containing elements that are in A but not in B, and A intersection B, containing elements common to both sets. Their union is A, so their cardinalities add. Thus n(A) = n(A − B) + n(A intersection B) = 32 + 18 = 50. Subtracting the values would be incorrect because the two given regions are separate parts of A, not quantities to be removed from one another. Therefore, option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
