With respect to the universal set \(U\), which of the following sets is equal to \(A\cap B'\)?
Answer and explanation
Correct answer: \(A\setminus B\)
The complement \(B'\), relative to the universal set \(U\), contains every element that is not in \(B\). Therefore \(A\cap B'\) consists precisely of elements that belong to \(A\) and do not belong to \(B\). This is the definition of the difference \(A\setminus B\). Option B reverses the sets, while option D describes elements in \(B\) but outside \(A\). Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
\(A\setminus B\)
Why is this the correct answer?
The complement \(B'\), relative to the universal set \(U\), contains every element that is not in \(B\). Therefore \(A\cap B'\) consists precisely of elements that belong to \(A\) and do not belong to \(B\). This is the definition of the difference \(A\setminus B\). Option B reverses the sets, while option D describes elements in \(B\) but outside \(A\). 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).
