If \(A\setminus B\subseteq A\cap C\), which conclusion must be true?
Answer and explanation
Correct answer: \(A\setminus B\subseteq C\)
The hypothesis says every element of \(A\setminus B\) belongs to the intersection \(A\cap C\). An element of an intersection belongs to both component sets, so every such element must belong to \(C\). Hence, by transitivity of inclusion, \(A\setminus B\subseteq C\). No relation between all of \(A\), \(B\), and \(C\) is forced.
Frequently asked questions
What is the correct answer to this question?
\(A\setminus B\subseteq C\)
Why is this the correct answer?
The hypothesis says every element of \(A\setminus B\) belongs to the intersection \(A\cap C\). An element of an intersection belongs to both component sets, so every such element must belong to \(C\). Hence, by transitivity of inclusion, \(A\setminus B\subseteq C\). No relation between all of \(A\), \(B\), and \(C\) is forced.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
