If A={∅,0}, what is P(A)?
Answer and explanation
Correct answer: {∅,{∅},{0},{∅,0}}
The set A has two distinct elements: the empty set ∅ and the number 0. A set with n elements has 2^n subsets, so P(A) has 2^2=4 elements. These are the empty subset ∅, the singleton {∅}, the singleton {0}, and the whole set {∅,0}. It is important not to confuse the element ∅ with the singleton set {∅}; they are different objects.
Frequently asked questions
What is the correct answer to this question?
{∅,{∅},{0},{∅,0}}
Why is this the correct answer?
The set A has two distinct elements: the empty set ∅ and the number 0. A set with n elements has 2^n subsets, so P(A) has 2^2=4 elements. These are the empty subset ∅, the singleton {∅}, the singleton {0}, and the whole set {∅,0}. It is important not to confuse the element ∅ with the singleton set {∅}; they are different objects.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
