If \(A-B=A\cap B'\), then what is \((A-B)'\) equal to?
Answer and explanation
Correct answer: \(A'\cup B\)
Use the given identity \(A-B=A\cap B'\). Taking complements on both sides gives \((A-B)'=(A\cap B')'\). De Morgan’s law changes the complement of an intersection into the union of the complements: \((A\cap B')'=A'\cup(B')'\). Since the complement of \(B'\) is \(B\), the result is \(A'\cup B\). Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
\(A'\cup B\)
Why is this the correct answer?
Use the given identity \(A-B=A\cap B'\). Taking complements on both sides gives \((A-B)'=(A\cap B')'\). De Morgan’s law changes the complement of an intersection into the union of the complements: \((A\cap B')'=A'\cup(B')'\). Since the complement of \(B'\) is \(B\), the result is \(A'\cup B\). Therefore, option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
