Assertion: If A ∩ B = ∅, then n(A ∪ B) = n(A) + n(B). Reason: Disjoint sets have no common elements or common region. Choose the correct option.
Answer and explanation
Correct answer: Both assertion and reason are true, and the reason is the correct explanation
Both statements are true, and the reason correctly explains the assertion. For any two finite sets, n(A ∪ B) = n(A) + n(B) − n(A ∩ B). If A and B are disjoint, their intersection is the empty set, so n(A ∩ B) = 0. Consequently, no element is counted in both sets, and the union contains the sum of the elements in A and B. Hence n(A ∪ B) = n(A) + n(B).
Frequently asked questions
What is the correct answer to this question?
Both assertion and reason are true, and the reason is the correct explanation
Why is this the correct answer?
Both statements are true, and the reason correctly explains the assertion. For any two finite sets, n(A ∪ B) = n(A) + n(B) − n(A ∩ B). If A and B are disjoint, their intersection is the empty set, so n(A ∩ B) = 0. Consequently, no element is counted in both sets, and the union contains the sum of the elements in A and B. Hence n(A ∪ B) = n(A) + n(B).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
