If \(A\cup B=A\), what is the correct conclusion?
Answer and explanation
Correct answer: \(B\subseteq A\)
Let \(x\) be any element of \(B\). By the definition of union, \(x\in A\cup B\). Since \(A\cup B=A\), this means \(x\in A\). Thus every element of \(B\) belongs to \(A\), so \(B\subseteq A\). The reverse inclusion or equality is not necessary; for example, \(A=\{1,2\}\) and \(B=\{1\}\) satisfy the condition but are not equal.
Frequently asked questions
What is the correct answer to this question?
\(B\subseteq A\)
Why is this the correct answer?
Let \(x\) be any element of \(B\). By the definition of union, \(x\in A\cup B\). Since \(A\cup B=A\), this means \(x\in A\). Thus every element of \(B\) belongs to \(A\), so \(B\subseteq A\). The reverse inclusion or equality is not necessary; for example, \(A=\{1,2\}\) and \(B=\{1\}\) satisfy the condition but are not equal.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
