If n(A ∩ B) = n(A) and n(A) > 0, what is the relation between A and B in a Venn diagram?
Answer and explanation
Correct answer: A ⊆ B
The intersection A ∩ B consists of elements common to both sets. If its cardinality equals n(A), every element of A is included in the intersection and therefore also belongs to B. Hence A is a subset of B, written A ⊆ B. The condition n(A) > 0 confirms that A is non-empty. Option B reverses the inclusion, while C and D contradict the non-empty intersection condition.
Frequently asked questions
What is the correct answer to this question?
A ⊆ B
Why is this the correct answer?
The intersection A ∩ B consists of elements common to both sets. If its cardinality equals n(A), every element of A is included in the intersection and therefore also belongs to B. Hence A is a subset of B, written A ⊆ B. The condition n(A) > 0 confirms that A is non-empty. Option B reverses the inclusion, while C and D contradict the non-empty intersection condition.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
