If U = {1,2,3,4,5,6} and A is a set such that A = Aᶜ, which statement is correct?
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Answer and explanation
Correct answer: No such A can exist
A set and its complement are always disjoint: A ∩ Aᶜ = ∅. If A = Aᶜ, then this would imply A ∩ A = ∅, so A would have to be empty. However, the complement of the empty set is U, and because U is nonempty, ∅ ≠ U. Therefore equality A = Aᶜ is impossible, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
No such A can exist
Why is this the correct answer?
A set and its complement are always disjoint: A ∩ Aᶜ = ∅. If A = Aᶜ, then this would imply A ∩ A = ∅, so A would have to be empty. However, the complement of the empty set is U, and because U is nonempty, ∅ ≠ U. Therefore equality A = Aᶜ is impossible, 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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