If the universal set is \(U=\{a,b,c,d,e,f\}\) and \(A'=\{b,d,f\}\), what is the set \(A\)?
Answer and explanation
Correct answer: \(\{a,c,e\}\)
The complement \(A'\) contains precisely those elements of the universal set \(U\) that are not in \(A\). Therefore, to recover \(A\), remove \(b,d,f\) from \(U\): \(A=U\setminus A'=\{a,b,c,d,e,f\}\setminus\{b,d,f\}=\{a,c,e\}\). Hence option A is correct. Option B is the complement itself, while option C incorrectly includes every element of \(U\).
Frequently asked questions
What is the correct answer to this question?
\(\{a,c,e\}\)
Why is this the correct answer?
The complement \(A'\) contains precisely those elements of the universal set \(U\) that are not in \(A\). Therefore, to recover \(A\), remove \(b,d,f\) from \(U\): \(A=U\setminus A'=\{a,b,c,d,e,f\}\setminus\{b,d,f\}=\{a,c,e\}\). Hence option A is correct. Option B is the complement itself, while option C incorrectly includes every element of \(U\).
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.
