If the universal set \(U=\{x:x\text{ is a digit}\}\) and \(A=\{0,2,4,6,8\}\), what is \(A^c\)?
Answer and explanation
Correct answer: \(\{1,3,5,7,9\}\)
The universal set of digits is \(U=\{0,1,2,3,4,5,6,7,8,9\}\). The complement \(A^c\) consists of every element of the universal set that does not belong to \(A\). Since \(A\) contains the even digits 0, 2, 4, 6, and 8, removing them from \(U\) leaves the odd digits 1, 3, 5, 7, and 9. Hence, \(A^c=\{1,3,5,7,9\}\), so option A is correct. The complement always depends on the stated universal set.
Frequently asked questions
What is the correct answer to this question?
\(\{1,3,5,7,9\}\)
Why is this the correct answer?
The universal set of digits is \(U=\{0,1,2,3,4,5,6,7,8,9\}\). The complement \(A^c\) consists of every element of the universal set that does not belong to \(A\). Since \(A\) contains the even digits 0, 2, 4, 6, and 8, removing them from \(U\) leaves the odd digits 1, 3, 5, 7, and 9. Hence, \(A^c=\{1,3,5,7,9\}\), so option A is correct. The complement always depends on the stated universal set.
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.
