If A = U, which statement about P(A) and P(U) is correct?
Answer and explanation
Correct answer: P(A) = P(U)
Equal sets have exactly the same elements and therefore exactly the same subsets. Since A = U, every subset of A is a subset of U and vice versa. Consequently their power sets are equal: P(A) = P(U). The other statements are false: a power set is not empty, P(U) is not generally a subset of A, and identical power sets have a non-empty intersection equal to themselves.
Frequently asked questions
What is the correct answer to this question?
P(A) = P(U)
Why is this the correct answer?
Equal sets have exactly the same elements and therefore exactly the same subsets. Since A = U, every subset of A is a subset of U and vice versa. Consequently their power sets are equal: P(A) = P(U). The other statements are false: a power set is not empty, P(U) is not generally a subset of A, and identical power sets have a non-empty intersection equal to themselves.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
