If, with respect to a universal set, a set A satisfies A = A′, which statement about A is correct?
Answer and explanation
Correct answer: No such set A can exist
For every set A in a universal set U, A and its complement A′ are disjoint, so A ∩ A′ = ∅. If A = A′, then this would imply A ∩ A = ∅, hence A = ∅. But the complement of the empty set is U, so A′ = U, and A = A′ would require ∅ = U, which is impossible for a nonempty universal set. Therefore no such set exists, and option D is correct.
Frequently asked questions
What is the correct answer to this question?
No such set A can exist
Why is this the correct answer?
For every set A in a universal set U, A and its complement A′ are disjoint, so A ∩ A′ = ∅. If A = A′, then this would imply A ∩ A = ∅, hence A = ∅. But the complement of the empty set is U, so A′ = U, and A = A′ would require ∅ = U, which is impossible for a nonempty universal set. Therefore no such set exists, and option D 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.
