Assertion: n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Reason: Elements of A ∩ B are counted twice in n(A) + n(B). Choose the correct option.
Answer and explanation
Correct answer: Both assertion and reason are true, and the reason is the correct explanation
Both the assertion and the reason are true. When n(A) and n(B) are added, every element common to A and B appears once in n(A) and once in n(B), so the intersection is counted twice. The union should count each element only once; therefore n(A ∩ B) must be subtracted once. This gives the inclusion–exclusion formula n(A ∪ B) = n(A) + n(B) − n(A ∩ B), so the reason correctly explains the assertion.
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 the assertion and the reason are true. When n(A) and n(B) are added, every element common to A and B appears once in n(A) and once in n(B), so the intersection is counted twice. The union should count each element only once; therefore n(A ∩ B) must be subtracted once. This gives the inclusion–exclusion formula n(A ∪ B) = n(A) + n(B) − n(A ∩ B), so the reason correctly explains the assertion.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
