If \(U=\{0,1,2,3,4\}\) and \(A=\{0,2,4\}\), find \(A^c\).
Answer and explanation
Correct answer: \(\{1,3\}\)
The complement of a set is determined relative to the stated universal set. Start with all elements of \(U\): 0, 1, 2, 3, and 4. Remove the elements belonging to \(A\), namely 0, 2, and 4. The elements left are 1 and 3, so \(A^c=\{1,3\}\). Therefore option A is correct. The presence of 0 in A does not change the procedure; zero is an ordinary element of the set.
Frequently asked questions
What is the correct answer to this question?
\(\{1,3\}\)
Why is this the correct answer?
The complement of a set is determined relative to the stated universal set. Start with all elements of \(U\): 0, 1, 2, 3, and 4. Remove the elements belonging to \(A\), namely 0, 2, and 4. The elements left are 1 and 3, so \(A^c=\{1,3\}\). Therefore option A is correct. The presence of 0 in A does not change the procedure; zero is an ordinary element of the 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.
