If (n(A\cup B)=n(A)), which conclusion is correct according to the Venn diagram?
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Answer and explanation
Correct answer: (B\subseteq A)
For finite sets, A∪B contains all elements of A and any additional elements contributed by B. If n(A∪B) equals n(A), B contributes no element outside A. Thus every element of B is already in A, which means B⊆A. The equality does not necessarily mean A=B, because B may be a proper subset of A.
Frequently asked questions
What is the correct answer to this question?
(B\subseteq A)
Why is this the correct answer?
For finite sets, A∪B contains all elements of A and any additional elements contributed by B. If n(A∪B) equals n(A), B contributes no element outside A. Thus every element of B is already in A, which means B⊆A. The equality does not necessarily mean A=B, because B may be a proper subset of A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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