If \(A\subseteq B\) and \(n(A)=n(B)\), where both sets are finite, what follows?
Answer and explanation
Correct answer: \(A=B\)
For finite sets, a proper subset must contain strictly fewer elements than the set containing it. Here A is contained in B, but both have the same finite cardinality. Therefore B cannot have any additional element outside A, so every element of B is already in A. Consequently, the two sets are equal: \(A=B\). This conclusion depends on finiteness.
Frequently asked questions
What is the correct answer to this question?
\(A=B\)
Why is this the correct answer?
For finite sets, a proper subset must contain strictly fewer elements than the set containing it. Here A is contained in B, but both have the same finite cardinality. Therefore B cannot have any additional element outside A, so every element of B is already in A. Consequently, the two sets are equal: \(A=B\). This conclusion depends on finiteness.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
