If n(A − B)=0 and n(A)>0, which relation between A and B is necessarily true in the Venn diagram?
Answer and explanation
Correct answer: A ⊆ B
A−B is the portion of A lying outside B. If its cardinality is zero, that portion contains no elements, so no element of A can lie outside B. Therefore every element of A belongs to B, which is exactly the definition of A⊆B. The condition n(A)>0 only confirms that A is nonempty; it does not imply B⊆A or disjointness.
Frequently asked questions
What is the correct answer to this question?
A ⊆ B
Why is this the correct answer?
A−B is the portion of A lying outside B. If its cardinality is zero, that portion contains no elements, so no element of A can lie outside B. Therefore every element of A belongs to B, which is exactly the definition of A⊆B. The condition n(A)>0 only confirms that A is nonempty; it does not imply B⊆A or disjointness.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
