If A = {7, 8}, why is {7, 8} ∈ 𝒫(A)?
Answer and explanation
Correct answer: Because every set is a subset of itself
The power set 𝒫(A) contains all subsets of A, including A itself. Since A = {7, 8}, the set {7, 8} is equal to A, and every set is a subset of itself: A ⊆ A. Therefore {7, 8} is an element of 𝒫(A). It is not an individual element of A; the individual elements of A are 7 and 8. Thus option A is correct.
Frequently asked questions
What is the correct answer to this question?
Because every set is a subset of itself
Why is this the correct answer?
The power set 𝒫(A) contains all subsets of A, including A itself. Since A = {7, 8}, the set {7, 8} is equal to A, and every set is a subset of itself: A ⊆ A. Therefore {7, 8} is an element of 𝒫(A). It is not an individual element of A; the individual elements of A are 7 and 8. Thus 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.
