If A = {10, 20, 30, 40}, in what form does the whole set A appear in P(A)?
Answer and explanation
Correct answer: As an element
A power set contains all subsets of the original set, including the original set itself. Every set is a subset of itself because each element of A belongs to A; symbolically, A ⊆ A. Therefore, when P(A) is formed, the complete set A appears as one element of P(A), written A ∈ P(A). It is not automatically a universal set.
Frequently asked questions
What is the correct answer to this question?
As an element
Why is this the correct answer?
A power set contains all subsets of the original set, including the original set itself. Every set is a subset of itself because each element of A belongs to A; symbolically, A ⊆ A. Therefore, when P(A) is formed, the complete set A appears as one element of P(A), written A ∈ P(A). It is not automatically a universal set.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
