If n(A) = 18, n(B) = 12, and n(A ∩ B) = 5, what is n(A ∪ B)?
Answer and explanation
Correct answer: 25
For two finite sets, the number of elements in their union is given by n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Substituting the given values gives 18 + 12 − 5 = 25. We subtract the intersection because the five common elements were counted once in n(A) and again in n(B). Hence, the correct answer is 25, option A.
Frequently asked questions
What is the correct answer to this question?
25
Why is this the correct answer?
For two finite sets, the number of elements in their union is given by n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Substituting the given values gives 18 + 12 − 5 = 25. We subtract the intersection because the five common elements were counted once in n(A) and again in n(B). Hence, the correct answer is 25, option 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).
