If U = {a,b,c,d} and A = {a,d}, how many elements does P(A′) have?
Answer and explanation
Correct answer: 4
First find the complement of A in U: A′ = U − A = {b,c}. Thus A′ has two elements. The power set of any finite set containing n elements has 2ⁿ elements, because every element has two choices—present or absent—in a subset. Therefore n(P(A′)) = 2² = 4. Option A gives the size of A′, not the size of its power set, so option B is correct.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
First find the complement of A in U: A′ = U − A = {b,c}. Thus A′ has two elements. The power set of any finite set containing n elements has 2ⁿ elements, because every element has two choices—present or absent—in a subset. Therefore n(P(A′)) = 2² = 4. Option A gives the size of A′, not the size of its power set, so option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
