Under which condition is P(A) ⊆ P(B) true?
Answer and explanation
Correct answer: A ⊆ B
If A ⊆ B, every element of A is also an element of B. Consequently, every subset of A is automatically a subset of B. Since P(A) and P(B) denote the sets of all subsets of A and B respectively, this proves P(A) ⊆ P(B). The converse is also true: because A belongs to P(A), the inclusion of power sets implies A ⊆ B. Thus option A gives the exact condition, whereas disjointness or an empty union is not generally required.
Frequently asked questions
What is the correct answer to this question?
A ⊆ B
Why is this the correct answer?
If A ⊆ B, every element of A is also an element of B. Consequently, every subset of A is automatically a subset of B. Since P(A) and P(B) denote the sets of all subsets of A and B respectively, this proves P(A) ⊆ P(B). The converse is also true: because A belongs to P(A), the inclusion of power sets implies A ⊆ B. Thus option A gives the exact condition, whereas disjointness or an empty union is not generally required.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
