If \(U=\{1,2,3,4,5,6\}\) and \(A'=\{2,6\}\), what is \(A\)?
Answer and explanation
Correct answer: \(\{1,3,4,5\}\)
The complement \(A'\) contains the elements of the universal set \(U\) that are not in \(A\). Therefore, to recover \(A\), remove the elements of \(A'\) from \(U\): \(A=U\setminus A'=\{1,2,3,4,5,6\}\setminus\{2,6\}=\{1,3,4,5\}\). Hence option B is correct. Option A is the complement itself, while C and D contain incorrect elements or omit required ones.
Frequently asked questions
What is the correct answer to this question?
\(\{1,3,4,5\}\)
Why is this the correct answer?
The complement \(A'\) contains the elements of the universal set \(U\) that are not in \(A\). Therefore, to recover \(A\), remove the elements of \(A'\) from \(U\): \(A=U\setminus A'=\{1,2,3,4,5,6\}\setminus\{2,6\}=\{1,3,4,5\}\). Hence option B is correct. Option A is the complement itself, while C and D contain incorrect elements or omit required ones.
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.
