If \(U\) is the set of all digits and \(A=\{0,2,4,6,8\}\), what is \(A'\)?
Answer and explanation
Correct answer: \(\{1,3,5,7,9\}\)
The set of all digits is \(U=\{0,1,2,3,4,5,6,7,8,9\}\). The set \(A\) contains all even digits, including zero. Its complement consists of the digits in \(U\) that are not in \(A\), namely the odd digits: \(A'=U\setminus A=\{1,3,5,7,9\}\). Therefore option A is correct. Option B omits zero only because it lists part of A, not its complement.
Frequently asked questions
What is the correct answer to this question?
\(\{1,3,5,7,9\}\)
Why is this the correct answer?
The set of all digits is \(U=\{0,1,2,3,4,5,6,7,8,9\}\). The set \(A\) contains all even digits, including zero. Its complement consists of the digits in \(U\) that are not in \(A\), namely the odd digits: \(A'=U\setminus A=\{1,3,5,7,9\}\). Therefore option A is correct. Option B omits zero only because it lists part of A, not its complement.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets.
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