If A = {∅, {∅}, 1}, which of the following is an element of P(A) but not an element of A?
Answer and explanation
Correct answer: {1, {∅}}
The power set P(A) consists of all subsets of A. The empty set ∅ is a subset of every set, and both {∅} and {1} are also subsets of A. However, the expression {1, {∅}} contains two elements, 1 and {∅}, and both are elements of A; therefore it is a subset of A and hence belongs to P(A). It is not itself an element of A, because the elements listed in A are ∅, {∅}, and 1. Thus option D is correct.
Frequently asked questions
What is the correct answer to this question?
{1, {∅}}
Why is this the correct answer?
The power set P(A) consists of all subsets of A. The empty set ∅ is a subset of every set, and both {∅} and {1} are also subsets of A. However, the expression {1, {∅}} contains two elements, 1 and {∅}, and both are elements of A; therefore it is a subset of A and hence belongs to P(A). It is not itself an element of A, because the elements listed in A are ∅, {∅}, and 1. Thus option D is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
