If A = {1, {2}, 3}, which one is an element of P(A)?
Answer and explanation
Correct answer: {1, {2}}
The power set P(A) contains every subset of A. The elements of A are 1, the set {2}, and 3; importantly, 2 itself is not an element of A. The set {1, {2}} uses the elements 1 and {2}, both of which belong to A, so it is a subset of A and therefore belongs to P(A). The other choices do not satisfy this condition, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
{1, {2}}
Why is this the correct answer?
The power set P(A) contains every subset of A. The elements of A are 1, the set {2}, and 3; importantly, 2 itself is not an element of A. The set {1, {2}} uses the elements 1 and {2}, both of which belong to A, so it is a subset of A and therefore belongs to P(A). The other choices do not satisfy this condition, so option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
