If \(A\cap B\ne\varnothing\) and \(A\setminus B=\varnothing\), which conclusion is correct?
Answer and explanation
Correct answer: \(A\subseteq B\) और \(A\ne\varnothing\)
The equality \(A\setminus B=\varnothing\) means that no element of \(A\) lies outside \(B\). By definition, this is equivalent to \(A\subseteq B\). The additional condition \(A\cap B\ne\varnothing\) says that the two sets share at least one element. Since every element of \(A\) is in \(B\), this also confirms that \(A\) is non-empty. Therefore option A is the correct conclusion.
Frequently asked questions
What is the correct answer to this question?
\(A\subseteq B\) और \(A\ne\varnothing\)
Why is this the correct answer?
The equality \(A\setminus B=\varnothing\) means that no element of \(A\) lies outside \(B\). By definition, this is equivalent to \(A\subseteq B\). The additional condition \(A\cap B\ne\varnothing\) says that the two sets share at least one element. Since every element of \(A\) is in \(B\), this also confirms that \(A\) is non-empty. Therefore option A is the correct conclusion.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
