Which statement is false for the complement of A?
Answer and explanation
Correct answer: A' is independent of the universal set
A complement is defined relative to a specified universal set U. The elements outside A may change when U changes, even if A itself remains the same. Hence A' is not independent of U. The other statements are standard complement identities: A union A' equals U, A intersection A' is empty, and A' equals U minus A. Therefore option A is false.
Frequently asked questions
What is the correct answer to this question?
A' is independent of the universal set
Why is this the correct answer?
A complement is defined relative to a specified universal set U. The elements outside A may change when U changes, even if A itself remains the same. Hence A' is not independent of U. The other statements are standard complement identities: A union A' equals U, A intersection A' is empty, and A' equals U minus A. Therefore 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.
