If \(A\setminus B\ne\varnothing\) and \(B\setminus A=\varnothing\), which statement is correct?
Answer and explanation
Correct answer: \(B\subset A\)
The condition \(B\setminus A=\varnothing\) means that no element of \(B\) lies outside \(A\); hence \(B\subseteq A\). The condition \(A\setminus B\ne\varnothing\) means that at least one element of \(A\) is not in \(B\), so \(A\ne B\). Combining these facts gives the proper inclusion \(B\subset A\), making option A correct.
Frequently asked questions
What is the correct answer to this question?
\(B\subset A\)
Why is this the correct answer?
The condition \(B\setminus A=\varnothing\) means that no element of \(B\) lies outside \(A\); hence \(B\subseteq A\). The condition \(A\setminus B\ne\varnothing\) means that at least one element of \(A\) is not in \(B\), so \(A\ne B\). Combining these facts gives the proper inclusion \(B\subset A\), making option A correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
