If U ≠ ∅, which statement cannot always be true?
Answer and explanation
Correct answer: A ∩ A' = U
A set and its complement are disjoint, so A ∩ A' = ∅ for every set A. Since the universal set U is explicitly non-empty, ∅ cannot equal U. The other statements are standard complement identities: A ∪ A' = U, (A')' = A, and the complement of U relative to U is ∅. Therefore, statement C cannot always be true.
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, so A ∩ A' = ∅ for every set A. Since the universal set U is explicitly non-empty, ∅ cannot equal U. The other statements are standard complement identities: A ∪ A' = U, (A')' = A, and the complement of U relative to U is ∅. Therefore, statement C cannot always be true.
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.
