If A = {∅, {1}, 2}, which of the following is an element of P(A)?
Answer and explanation
Correct answer: {∅, 2}
The elements of A are ∅, {1}, and 2. An element of P(A) must be a subset whose every member is one of these three objects. The set {∅, 2} uses two actual elements of A, so it is a subset of A and therefore belongs to P(A). In contrast, 1 is not an element of A, and neither {1,2} nor {{2}} satisfies the subset condition. Thus A is correct.
Frequently asked questions
What is the correct answer to this question?
{∅, 2}
Why is this the correct answer?
The elements of A are ∅, {1}, and 2. An element of P(A) must be a subset whose every member is one of these three objects. The set {∅, 2} uses two actual elements of A, so it is a subset of A and therefore belongs to P(A). In contrast, 1 is not an element of A, and neither {1,2} nor {{2}} satisfies the subset condition. Thus 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.
