Which condition is required for P(A′) = P(A), where the complement is taken with respect to U?
Answer and explanation
Correct answer: A = A′
For any sets X and Y, P(X) = P(Y) implies X = Y, because each set can be recovered as the union of all members of its power set. Therefore P(A′) = P(A) requires A′ = A. In an ordinary nonempty universal set, a set cannot equal its own complement, because A and A′ are disjoint; thus this equality is possible only in the degenerate case U = ∅. Among the given conditions, C states the required condition.
Frequently asked questions
What is the correct answer to this question?
A = A′
Why is this the correct answer?
For any sets X and Y, P(X) = P(Y) implies X = Y, because each set can be recovered as the union of all members of its power set. Therefore P(A′) = P(A) requires A′ = A. In an ordinary nonempty universal set, a set cannot equal its own complement, because A and A′ are disjoint; thus this equality is possible only in the degenerate case U = ∅. Among the given conditions, C states the required condition.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
