If n(A ∪ B) = n(B), which relation is correct according to the Venn diagram?
Answer and explanation
Correct answer: A ⊆ B
The union A ∪ B contains B and possibly some additional elements from A. If its cardinality is exactly equal to n(B), there can be no elements of A outside B. Equivalently, using n(A ∪ B) = n(A) + n(B) − n(A ∩ B), the given equality gives n(A) = n(A ∩ B), so every element of A lies in B. Therefore A ⊆ B, making option A correct.
Frequently asked questions
What is the correct answer to this question?
A ⊆ B
Why is this the correct answer?
The union A ∪ B contains B and possibly some additional elements from A. If its cardinality is exactly equal to n(B), there can be no elements of A outside B. Equivalently, using n(A ∪ B) = n(A) + n(B) − n(A ∩ B), the given equality gives n(A) = n(A ∩ B), so every element of A lies in B. Therefore A ⊆ B, making option A correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
