If A = {1, 2} and the universal set U = {1, 2, 3}, what is P(A′)?
Answer and explanation
Correct answer: {∅, {3}}
First find the complement relative to U: A′ = U − A = {3}. The power set of a one-element set contains exactly two subsets: the empty set and the set itself. Hence P(A′) = P({3}) = {∅, {3}}. Option B is incorrect because 3 is an element, not a subset written as {3}; the other options do not represent this power set.
Frequently asked questions
What is the correct answer to this question?
{∅, {3}}
Why is this the correct answer?
First find the complement relative to U: A′ = U − A = {3}. The power set of a one-element set contains exactly two subsets: the empty set and the set itself. Hence P(A′) = P({3}) = {∅, {3}}. Option B is incorrect because 3 is an element, not a subset written as {3}; the other options do not represent this power set.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
