If \(U=\{1,2,3,4,5,6,7\}\) and \(A'=\{2,4,6\}\), what is \(A\)?
Answer and explanation
Correct answer: \(\{1,3,5,7\}\)
The set \(A'\) contains the elements of the universal set that are not in \(A\). Since \(U=\{1,2,3,4,5,6,7\}\) and \(A'=\{2,4,6\}\), the elements remaining in \(U\) are \(1,3,5,7\). These remaining elements form \(A\). Equivalently, \(A=U\setminus A'\). Hence \(A=\{1,3,5,7\}\), so option A is correct.
Frequently asked questions
What is the correct answer to this question?
\(\{1,3,5,7\}\)
Why is this the correct answer?
The set \(A'\) contains the elements of the universal set that are not in \(A\). Since \(U=\{1,2,3,4,5,6,7\}\) and \(A'=\{2,4,6\}\), the elements remaining in \(U\) are \(1,3,5,7\). These remaining elements form \(A\). Equivalently, \(A=U\setminus A'\). Hence \(A=\{1,3,5,7\}\), so 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.
