If A = {∅, {∅}, 1}, which of the following sets is an element of the power set P(A) but not an element of A?
Answer and explanation
Correct answer: {∅, 1}
The power set P(A) is the set of all subsets of A. The set {∅, 1} contains two elements, ∅ and 1, and both of them are elements of A; therefore, {∅, 1} is a subset of A and belongs to P(A). However, {∅, 1} itself is not listed among the three elements of A. In contrast, 1, ∅, and {∅} are all elements of A. Hence, option B is the only correct answer.
Frequently asked questions
What is the correct answer to this question?
{∅, 1}
Why is this the correct answer?
The power set P(A) is the set of all subsets of A. The set {∅, 1} contains two elements, ∅ and 1, and both of them are elements of A; therefore, {∅, 1} is a subset of A and belongs to P(A). However, {∅, 1} itself is not listed among the three elements of A. In contrast, 1, ∅, and {∅} are all elements of A. Hence, option B is the only correct answer.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
