Which statement is always false if U ≠ ∅?
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Answer and explanation
Correct answer: A ∩ A′ = U
A set and its complement are disjoint by definition, so A ∩ A′ is always the empty set. Also, A ∪ A′ = U and (A′)′ = A are standard complement identities. Since the universal set U is non-empty, the empty set cannot equal U. Therefore, A ∩ A′ = U is always false.
Frequently asked questions
What is the correct answer to this question?
A ∩ A′ = U
Why is this the correct answer?
A set and its complement are disjoint by definition, so A ∩ A′ is always the empty set. Also, A ∪ A′ = U and (A′)′ = A are standard complement identities. Since the universal set U is non-empty, the empty set cannot equal U. Therefore, A ∩ A′ = U is always false.
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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