If \(A\cup A'=U\) and \(A\cap A'=\varnothing\), what is the correct meaning of \(A'\)?
Answer and explanation
Correct answer: All elements of \(U\) that are not in \(A\)
The two given relations describe a complement: \(A\cup A'=U\) means that together A and \(A'\) contain every element of the universe, while \(A\cap A'=\varnothing\) means that they have no common element. Therefore \(A'\) consists exactly of the elements of \(U\) that do not belong to A, and it can be written as \(U\setminus A\). Option A states this definition. Option B is impossible for a subset A of U, and C and D do not express the complement.
Frequently asked questions
What is the correct answer to this question?
All elements of \(U\) that are not in \(A\)
Why is this the correct answer?
The two given relations describe a complement: \(A\cup A'=U\) means that together A and \(A'\) contain every element of the universe, while \(A\cap A'=\varnothing\) means that they have no common element. Therefore \(A'\) consists exactly of the elements of \(U\) that do not belong to A, and it can be written as \(U\setminus A\). Option A states this definition. Option B is impossible for a subset A of U, and C and D do not express the complement.
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.
