If U is enlarged and A remains the same, what may happen to A^c?
Answer and explanation
Correct answer: New elements may be added to A^c.
A complement is defined relative to a particular universal set: A^c=U−A. If U is enlarged while A stays unchanged, any newly included elements that are not members of A will belong to the new complement. Thus the complement may gain new elements. It is not necessarily empty, equal to A, or unchanged. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
New elements may be added to A^c.
Why is this the correct answer?
A complement is defined relative to a particular universal set: A^c=U−A. If U is enlarged while A stays unchanged, any newly included elements that are not members of A will belong to the new complement. Thus the complement may gain new elements. It is not necessarily empty, equal to A, or unchanged. Therefore, 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.
