If U = {1, 2, 3, 4, 5} and A = {2, 3}, the power set of A′ will be based on which set?
Answer and explanation
Correct answer: {1, 4, 5}
The governing concepts are complement relative to a universal set and the power set of a set. Since A′ contains elements of U that are not in A, remove 2 and 3 from U = {1, 2, 3, 4, 5}; hence A′ = {1, 4, 5}. The power set P(A′) consists of all subsets generated from these three elements. Therefore it is based on {1, 4, 5}, making option B correct. Option C is U itself, not its complement.
Frequently asked questions
What is the correct answer to this question?
{1, 4, 5}
Why is this the correct answer?
The governing concepts are complement relative to a universal set and the power set of a set. Since A′ contains elements of U that are not in A, remove 2 and 3 from U = {1, 2, 3, 4, 5}; hence A′ = {1, 4, 5}. The power set P(A′) consists of all subsets generated from these three elements. Therefore it is based on {1, 4, 5}, making option B correct. Option C is U itself, not its complement.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
