If A ⊆ U, what is (A′ ∩ A)′ equal to?
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Answer and explanation
Correct answer: U
A set and its complement are disjoint, so A′ ∩ A = ∅. The complement is taken relative to the universal set U. The complement of the empty set is the entire universal set, because every element of U is outside ∅. Therefore (A′ ∩ A)′ = (∅)′ = U, making option A correct.
Frequently asked questions
What is the correct answer to this question?
U
Why is this the correct answer?
A set and its complement are disjoint, so A′ ∩ A = ∅. The complement is taken relative to the universal set U. The complement of the empty set is the entire universal set, because every element of U is outside ∅. Therefore (A′ ∩ A)′ = (∅)′ = U, making option A 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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