If U is the universal set and A is a subset of U, what is U − A equal to?
Answer and explanation
Correct answer: Aᶜ
The relative difference U − A contains all elements that are in U but not in A. This is exactly the definition of the complement of A with respect to U, so U − A = Aᶜ. Option B gives the removed set itself, and option C incorrectly retains the elements of A. Option D occurs only in the special case A = U, not for every subset A.
Frequently asked questions
What is the correct answer to this question?
Aᶜ
Why is this the correct answer?
The relative difference U − A contains all elements that are in U but not in A. This is exactly the definition of the complement of A with respect to U, so U − A = Aᶜ. Option B gives the removed set itself, and option C incorrectly retains the elements of A. Option D occurs only in the special case A = U, not for every subset A.
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.
