If \(A\subset B\) and \(B\subset A\), what is the correct conclusion?
Answer and explanation
Correct answer: \(A=B\)
If \(A\subseteq B\), every element of A belongs to B. If at the same time \(B\subseteq A\), every element of B belongs to A. Thus neither set contains an element absent from the other, so they have exactly the same elements and must be equal: \(A=B\). This is the standard two-inclusion method for proving equality of sets. The conclusion says nothing about whether the sets are finite or infinite. Their intersection is actually the common set itself, not the empty set.
Frequently asked questions
What is the correct answer to this question?
\(A=B\)
Why is this the correct answer?
If \(A\subseteq B\), every element of A belongs to B. If at the same time \(B\subseteq A\), every element of B belongs to A. Thus neither set contains an element absent from the other, so they have exactly the same elements and must be equal: \(A=B\). This is the standard two-inclusion method for proving equality of sets. The conclusion says nothing about whether the sets are finite or infinite. Their intersection is actually the common set itself, not the empty set.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
