If \(U=\{0,1,2,3,4\}\) and \(A=\{0,2,4\}\), how many elements are in \(A'\)?
Answer and explanation
Correct answer: 2
The complement \(A'\) contains all elements of the universal set \(U\) that are not present in \(A\). From \(U=\{0,1,2,3,4\}\), remove the elements of \(A=\{0,2,4\}\). The remaining elements are \(A'=U\setminus A=\{1,3\}\), so \(A'\) has 2 elements. The same result follows from \(n(A')=n(U)-n(A)=5-3=2\). Hence option B is correct.
Frequently asked questions
What is the correct answer to this question?
2
Why is this the correct answer?
The complement \(A'\) contains all elements of the universal set \(U\) that are not present in \(A\). From \(U=\{0,1,2,3,4\}\), remove the elements of \(A=\{0,2,4\}\). The remaining elements are \(A'=U\setminus A=\{1,3\}\), so \(A'\) has 2 elements. The same result follows from \(n(A')=n(U)-n(A)=5-3=2\). Hence option B 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.
