If \(U=\{\text{red},\text{blue},\text{green},\text{yellow}\}\) and \(A=\{\text{red},\text{yellow}\}\), what is \(A^c\)?
Answer and explanation
Correct answer: \(\{\text{blue},\text{green}\}\)
The complement of \(A\) is found by taking all elements of \(U\) and removing the elements that belong to \(A\). The universal set contains red, blue, green, and yellow, while \(A\) contains red and yellow. The remaining elements are blue and green. Hence, \(A^c=\{\text{blue},\text{green}\}\), so option A is correct.
Frequently asked questions
What is the correct answer to this question?
\(\{\text{blue},\text{green}\}\)
Why is this the correct answer?
The complement of \(A\) is found by taking all elements of \(U\) and removing the elements that belong to \(A\). The universal set contains red, blue, green, and yellow, while \(A\) contains red and yellow. The remaining elements are blue and green. Hence, \(A^c=\{\text{blue},\text{green}\}\), so option A 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.
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