For subsets A and B of a universal set U, if A' = B', which conclusion is necessarily true?
Answer and explanation
Correct answer: A = B
Both complements are taken with respect to the same universal set U. Taking the complement of both sides of A' = B' gives (A')' = (B')'. By the double-complement law, (A')' = A and (B')' = B, so A = B. The other statements do not necessarily follow: equal sets need not be disjoint, their union need not be U, and A' = B is a different condition.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
Both complements are taken with respect to the same universal set U. Taking the complement of both sides of A' = B' gives (A')' = (B')'. By the double-complement law, (A')' = A and (B')' = B, so A = B. The other statements do not necessarily follow: equal sets need not be disjoint, their union need not be U, and A' = B is a different condition.
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.
