If \(A\) and \(B\) are subsets of the universal set \(U\), what is the complement of \(A\setminus B\) with respect to \(U\)?
Answer and explanation
Correct answer: \(A'\cup B\)
Rewrite the difference as an intersection with a complement: \(A\setminus B=A\cap B'\). Taking the complement with respect to \(U\) and applying De Morgan’s law gives \((A\setminus B)'=(A\cap B')'=A'\cup(B')'=A'\cup B\). Thus the required complement contains everything outside \(A\), together with all elements of \(B\), and option A is correct.
Frequently asked questions
What is the correct answer to this question?
\(A'\cup B\)
Why is this the correct answer?
Rewrite the difference as an intersection with a complement: \(A\setminus B=A\cap B'\). Taking the complement with respect to \(U\) and applying De Morgan’s law gives \((A\setminus B)'=(A\cap B')'=A'\cup(B')'=A'\cup B\). Thus the required complement contains everything outside \(A\), together with all elements of \(B\), and 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).
