If \(A\subseteq B\subseteq C\), then what is \(A\cap(C\setminus B)\)?
Answer and explanation
Correct answer: \(\varnothing\)
The condition \(A\subseteq B\) means every element of \(A\) is already an element of \(B\). On the other hand, \(C\setminus B\) contains elements of \(C\) that are specifically not in \(B\). No element can therefore belong to both \(A\) and \(C\setminus B\). Their intersection is empty, so \(A\cap(C\setminus B)=\varnothing\). Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
\(\varnothing\)
Why is this the correct answer?
The condition \(A\subseteq B\) means every element of \(A\) is already an element of \(B\). On the other hand, \(C\setminus B\) contains elements of \(C\) that are specifically not in \(B\). No element can therefore belong to both \(A\) and \(C\setminus B\). Their intersection is empty, so \(A\cap(C\setminus B)=\varnothing\). Hence option A is 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).
