If U = (-5,5] and A = [-1,3), what is Aᶜ?
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Answer and explanation
Correct answer: (-5,-1) ∪ [3,5]
The complement is formed relative to U = (-5,5]. In A = [-1,3), the endpoint -1 is included, so it must be excluded from Aᶜ. The endpoint 3 is excluded from A, so it must be included in Aᶜ. Thus the part before A is (-5,-1), and the part after A is [3,5]. Therefore Aᶜ = (-5,-1) ∪ [3,5].
Frequently asked questions
What is the correct answer to this question?
(-5,-1) ∪ [3,5]
Why is this the correct answer?
The complement is formed relative to U = (-5,5]. In A = [-1,3), the endpoint -1 is included, so it must be excluded from Aᶜ. The endpoint 3 is excluded from A, so it must be included in Aᶜ. Thus the part before A is (-5,-1), and the part after A is [3,5]. Therefore Aᶜ = (-5,-1) ∪ [3,5].
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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