If \(A\cup B=A\), which conclusion is always true?
Answer and explanation
Correct answer: \(B\subseteq A\)
The union \(A\cup B\) contains every element of \(B\). If this union is equal to \(A\), then every element of \(B\) must also be an element of \(A\). This is precisely the definition of \(B\subseteq A\). The reverse inclusion, \(A\subseteq B\), is not necessary; for example, \(A=\{1,2\}\) and \(B=\{1\}\) satisfy the condition. The intersection need not be empty, and a complement relation cannot be inferred.
Frequently asked questions
What is the correct answer to this question?
\(B\subseteq A\)
Why is this the correct answer?
The union \(A\cup B\) contains every element of \(B\). If this union is equal to \(A\), then every element of \(B\) must also be an element of \(A\). This is precisely the definition of \(B\subseteq A\). The reverse inclusion, \(A\subseteq B\), is not necessary; for example, \(A=\{1,2\}\) and \(B=\{1\}\) satisfy the condition. The intersection need not be empty, and a complement relation cannot be inferred.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
