Given \(U=\{1,2,3,4,5,6,7\}\) and \(A=\{1,3,5,7\}\), what is the complement \(A^c\)?
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Answer and explanation
Correct answer: \(\{2,4,6\}\)
The complement \(A^c\) contains all elements of the universal set U that are not members of A. Starting with U = {1,2,3,4,5,6,7} and removing 1, 3, 5, and 7 leaves {2,4,6}. Hence \(A^c=\{2,4,6\}\). The complement depends on the chosen universal set, so it cannot be identified without considering U.
Frequently asked questions
What is the correct answer to this question?
\(\{2,4,6\}\)
Why is this the correct answer?
The complement \(A^c\) contains all elements of the universal set U that are not members of A. Starting with U = {1,2,3,4,5,6,7} and removing 1, 3, 5, and 7 leaves {2,4,6}. Hence \(A^c=\{2,4,6\}\). The complement depends on the chosen universal set, so it cannot be identified without considering U.
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.
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