If n(A ∪ B) = n(A) + n(B), which conclusion is correct according to the Venn diagram?
Answer and explanation
Correct answer: A ∩ B = ∅
The cardinality formula for two sets is n(A ∪ B) = n(A) + n(B) − n(A ∩ B). In the question, the union equals the simple sum, so the subtracted intersection term must be zero. Therefore n(A ∩ B) = 0, which means that A and B have no common element. In a Venn diagram, their circles do not overlap; such sets are called disjoint sets.
Frequently asked questions
What is the correct answer to this question?
A ∩ B = ∅
Why is this the correct answer?
The cardinality formula for two sets is n(A ∪ B) = n(A) + n(B) − n(A ∩ B). In the question, the union equals the simple sum, so the subtracted intersection term must be zero. Therefore n(A ∩ B) = 0, which means that A and B have no common element. In a Venn diagram, their circles do not overlap; such sets are called disjoint sets.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
