If n(A ∩ B) = n(A), which relation must be true?
Answer and explanation
Correct answer: A ⊆ B
The intersection A ∩ B can contain only elements that are already in A. If n(A ∩ B) equals n(A), then the intersection contains as many elements as the whole set A. Therefore every element of A must also lie in B, which gives A ⊆ B. The sets do not have to be equal; B may contain additional elements outside A. Hence option A is necessary and correct.
Frequently asked questions
What is the correct answer to this question?
A ⊆ B
Why is this the correct answer?
The intersection A ∩ B can contain only elements that are already in A. If n(A ∩ B) equals n(A), then the intersection contains as many elements as the whole set A. Therefore every element of A must also lie in B, which gives A ⊆ B. The sets do not have to be equal; B may contain additional elements outside A. Hence option A is necessary and correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
