Which formula correctly gives the number of elements belonging to exactly two of three sets?
Answer and explanation
Correct answer: n(A ∩ B)+n(B ∩ C)+n(C ∩ A)−3n(A ∩ B ∩ C)
Each pairwise intersection includes the elements common to all three sets. If the three pairwise intersections are added, every element in the triple intersection is counted three times, although it belongs to none of the exactly-two regions. Subtracting 3n(A ∩ B ∩ C) removes these triple counts and leaves only elements in exactly two sets. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
n(A ∩ B)+n(B ∩ C)+n(C ∩ A)−3n(A ∩ B ∩ C)
Why is this the correct answer?
Each pairwise intersection includes the elements common to all three sets. If the three pairwise intersections are added, every element in the triple intersection is counted three times, although it belongs to none of the exactly-two regions. Subtracting 3n(A ∩ B ∩ C) removes these triple counts and leaves only elements in exactly two sets. Hence option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
