If n(A) = 12, n(B) = 9, and n(A ∩ B) = 4, what is n(A ∪ B)?
Answer and explanation
Correct answer: 17
For two finite sets, the inclusion–exclusion formula is n(A ∪ B) = n(A) + n(B) − n(A ∩ B). The intersection is subtracted because its elements have been counted once in n(A) and once again in n(B). Substituting the given values gives 12 + 9 − 4 = 17. Thus the union contains 17 elements, and option A is correct. Adding 12 and 9 without subtraction would double-count the four common elements.
Frequently asked questions
What is the correct answer to this question?
17
Why is this the correct answer?
For two finite sets, the inclusion–exclusion formula is n(A ∪ B) = n(A) + n(B) − n(A ∩ B). The intersection is subtracted because its elements have been counted once in n(A) and once again in n(B). Substituting the given values gives 12 + 9 − 4 = 17. Thus the union contains 17 elements, and option A is correct. Adding 12 and 9 without subtraction would double-count the four common elements.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
