If \(U=\{1,2,3,4,5,6,7,8\}\) and \(A=\{x:x\in U,\ x\text{ is even}\}\), which set is \(A'\)?
Answer and explanation
Correct answer: \(\{1,3,5,7\}\)
The set-builder condition says that \(A\) contains the even elements of \(U\), namely \(\{2,4,6,8\}\). The complement \(A'\) contains every element of \(U\) that is not even. Within this finite universal set, those elements are the odd numbers \(1,3,5,7\). Hence \(A'=\{1,3,5,7\}\), making option A correct.
Frequently asked questions
What is the correct answer to this question?
\(\{1,3,5,7\}\)
Why is this the correct answer?
The set-builder condition says that \(A\) contains the even elements of \(U\), namely \(\{2,4,6,8\}\). The complement \(A'\) contains every element of \(U\) that is not even. Within this finite universal set, those elements are the odd numbers \(1,3,5,7\). Hence \(A'=\{1,3,5,7\}\), making option A 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.
