When \(A\subseteq B\), what is \(A\cap B\) equal to?
Answer and explanation
Correct answer: \(A\)
The intersection contains elements common to both sets. Since \(A\subseteq B\), every element of A is also an element of B. Thus all elements of A are common to A and B, while B may contain additional elements that are not in A. Therefore, \(A\cap B=A\). The answer does not depend on the particular elements, only on the subset relationship.
Frequently asked questions
What is the correct answer to this question?
\(A\)
Why is this the correct answer?
The intersection contains elements common to both sets. Since \(A\subseteq B\), every element of A is also an element of B. Thus all elements of A are common to A and B, while B may contain additional elements that are not in A. Therefore, \(A\cap B=A\). The answer does not depend on the particular elements, only on the subset relationship.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
