If the universal set is \(U=\{1,2,\ldots,10\}\) and \(A=\{1,3,5,7,9\}\), what is \((A')'\)?
Answer and explanation
Correct answer: \(\{1,3,5,7,9\}\)
The complement of a set is taken with respect to the stated universal set. Here, \(A'=\{2,4,6,8,10\}\), because these are the elements of \(U\) that are not in \(A\). Taking the complement again returns all the original elements of \(A\). Therefore, the double-complement law gives \((A')'=A=\{1,3,5,7,9\}\), so option A is correct. Option B represents only the first complement.
Frequently asked questions
What is the correct answer to this question?
\(\{1,3,5,7,9\}\)
Why is this the correct answer?
The complement of a set is taken with respect to the stated universal set. Here, \(A'=\{2,4,6,8,10\}\), because these are the elements of \(U\) that are not in \(A\). Taking the complement again returns all the original elements of \(A\). Therefore, the double-complement law gives \((A')'=A=\{1,3,5,7,9\}\), so option A is correct. Option B represents only the first 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.
