Which expression is equal to \(A\setminus(B\setminus C)\)?
Answer and explanation
Correct answer: \((A\setminus B)\cup(A\cap C)\)
An element of \(A\setminus(B\setminus C)\) is in \(A\), but it is not in \(B\setminus C\). Being outside \(B\setminus C\) means either being outside \(B\), or being in \(C\). Therefore the result consists of elements in \(A\setminus B\) together with elements in \(A\cap C\). Hence \(A\setminus(B\setminus C)=(A\setminus B)\cup(A\cap C)\), making option A correct.
Frequently asked questions
What is the correct answer to this question?
\((A\setminus B)\cup(A\cap C)\)
Why is this the correct answer?
An element of \(A\setminus(B\setminus C)\) is in \(A\), but it is not in \(B\setminus C\). Being outside \(B\setminus C\) means either being outside \(B\), or being in \(C\). Therefore the result consists of elements in \(A\setminus B\) together with elements in \(A\cap C\). Hence \(A\setminus(B\setminus C)=(A\setminus B)\cup(A\cap C)\), 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).
