If \(A-B=\varnothing\), which conclusion is correct?
Answer and explanation
Correct answer: \(A\subseteq B\)
The difference \(A-B\) contains elements that are in A but not in B. If this difference is empty, then no element of A lies outside B. Therefore every element of A is also an element of B, which is exactly the definition of \(A\subseteq B\). The reverse inclusion is not guaranteed, and the sets need not be disjoint or empty. Thus option A is the only conclusion that must be true.
Frequently asked questions
What is the correct answer to this question?
\(A\subseteq B\)
Why is this the correct answer?
The difference \(A-B\) contains elements that are in A but not in B. If this difference is empty, then no element of A lies outside B. Therefore every element of A is also an element of B, which is exactly the definition of \(A\subseteq B\). The reverse inclusion is not guaranteed, and the sets need not be disjoint or empty. Thus option A is the only conclusion that must be true.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
