If \(U=\{2,3,4,5,6\}\) and \(A=\{3,6\}\), what is \(A^c\)?
Answer and explanation
Correct answer: \(\{2,4,5\}\)
The complement A^c consists of all elements that belong to the universal set U but do not belong to A. Starting with U={2,3,4,5,6}, remove the elements 3 and 6 because they are in A. The remaining elements are 2, 4, and 5, so A^c={2,4,5}. Option B is A itself, option C incorrectly retains elements of A, and option D is not empty.
Frequently asked questions
What is the correct answer to this question?
\(\{2,4,5\}\)
Why is this the correct answer?
The complement A^c consists of all elements that belong to the universal set U but do not belong to A. Starting with U={2,3,4,5,6}, remove the elements 3 and 6 because they are in A. The remaining elements are 2, 4, and 5, so A^c={2,4,5}. Option B is A itself, option C incorrectly retains elements of A, and option D is not empty.
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.
