Which of the following statements is false?
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Answer and explanation
Correct answer: A ∩ Aᶜ = U
The complement Aᶜ contains all elements of the universal set U that are not in A. Therefore, no element can belong to both A and Aᶜ, so A ∩ Aᶜ = ∅, not U. The other statements are standard complement properties: A ∪ Aᶜ = U, (Aᶜ)ᶜ = A, and Aᶜ is always a subset of U. Hence option A is false.
Frequently asked questions
What is the correct answer to this question?
A ∩ Aᶜ = U
Why is this the correct answer?
The complement Aᶜ contains all elements of the universal set U that are not in A. Therefore, no element can belong to both A and Aᶜ, so A ∩ Aᶜ = ∅, not U. The other statements are standard complement properties: A ∪ Aᶜ = U, (Aᶜ)ᶜ = A, and Aᶜ is always a subset of U. Hence option A is 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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