With respect to the universal set \(U\), for a set \(A\), what is \((A')'\) equal to?
Answer and explanation
Correct answer: \(A\)
The complement of \(A\) is defined as \(A'=U\setminus A\), meaning that it contains all elements of the universal set that are not in \(A\). Taking the complement again gives \((A')'=U\setminus(U\setminus A)=A\). Thus, the double-complement law states that complementing a set twice returns the original set. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
\(A\)
Why is this the correct answer?
The complement of \(A\) is defined as \(A'=U\setminus A\), meaning that it contains all elements of the universal set that are not in \(A\). Taking the complement again gives \((A')'=U\setminus(U\setminus A)=A\). Thus, the double-complement law states that complementing a set twice returns the original set. 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.
