If U is the universal set and A ⊆ U, why is P(A) ⊆ P(U) true?
Answer and explanation
Correct answer: Every subset of A is also a subset of U
A ⊆ U means that every element of A is also an element of U. Now take any element X of P(A). By definition, X is a subset of A, so every element of X belongs to A and therefore also belongs to U. Hence X is a subset of U, which means X ∈ P(U). Since this holds for every X in P(A), we conclude that P(A) ⊆ P(U).
Frequently asked questions
What is the correct answer to this question?
Every subset of A is also a subset of U
Why is this the correct answer?
A ⊆ U means that every element of A is also an element of U. Now take any element X of P(A). By definition, X is a subset of A, so every element of X belongs to A and therefore also belongs to U. Hence X is a subset of U, which means X ∈ P(U). Since this holds for every X in P(A), we conclude that P(A) ⊆ P(U).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
