If U changes but A remains the same, which statement about Aᶜ is correct?
Answer and explanation
Correct answer: Aᶜ may change
The complement of A is defined relative to a specified universal set: Aᶜ = U \ A. Consequently, even if the elements of A remain unchanged, changing U can add or remove elements from the complement. For example, if U expands by adding an element not in A, that element enters Aᶜ. Hence Aᶜ may change, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
Aᶜ may change
Why is this the correct answer?
The complement of A is defined relative to a specified universal set: Aᶜ = U \ A. Consequently, even if the elements of A remain unchanged, changing U can add or remove elements from the complement. For example, if U expands by adding an element not in A, that element enters Aᶜ. Hence Aᶜ may change, so option A is correct.
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.
