If A = {2, 4, 6}, is A itself an element of P(A)?
Answer and explanation
Correct answer: Yes, because A ⊆ A
The power set P(A) is the collection of every subset of A. A set is always a subset of itself, so A ⊆ A. Consequently, A is one of the members of P(A), which means A ∈ P(A). The other choices confuse elements with subsets or introduce irrelevant conditions. A set does not need to be universal, empty, or have a particular size to belong to its own power set.
Frequently asked questions
What is the correct answer to this question?
Yes, because A ⊆ A
Why is this the correct answer?
The power set P(A) is the collection of every subset of A. A set is always a subset of itself, so A ⊆ A. Consequently, A is one of the members of P(A), which means A ∈ P(A). The other choices confuse elements with subsets or introduce irrelevant conditions. A set does not need to be universal, empty, or have a particular size to belong to its own power set.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
