If \(A\setminus B=A\setminus C\) and \(B\subseteq C\), which conclusion must be true?
Answer and explanation
Correct answer: \(A\cap C\subseteq B\cup A^c\)
Because \(B\subseteq C\), any element of \(A\) that lies in \(C\) but not in \(B\) would belong to \(A\setminus B\) but not to \(A\setminus C\), contradicting their equality. Thus every element of \(A\cap C\) is either in \(B\) or outside \(A\), which is written \(A\cap C\subseteq B\cup A^c\).
Frequently asked questions
What is the correct answer to this question?
\(A\cap C\subseteq B\cup A^c\)
Why is this the correct answer?
Because \(B\subseteq C\), any element of \(A\) that lies in \(C\) but not in \(B\) would belong to \(A\setminus B\) but not to \(A\setminus C\), contradicting their equality. Thus every element of \(A\cap C\) is either in \(B\) or outside \(A\), which is written \(A\cap C\subseteq B\cup A^c\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
