If A⊆B, which relation between P(A) and P(B) is always true?
Answer and explanation
Correct answer: P(A)⊆P(B)
The statement A⊆B means every element of A is also an element of B. Take any set X in P(A). By definition, X⊆A. Since every element of A belongs to B, all elements of X also belong to B, so X⊆B. Therefore X∈P(B). This proves P(A)⊆P(B), making option A always true. Equality occurs only in special cases, such as A=B.
Frequently asked questions
What is the correct answer to this question?
P(A)⊆P(B)
Why is this the correct answer?
The statement A⊆B means every element of A is also an element of B. Take any set X in P(A). By definition, X⊆A. Since every element of A belongs to B, all elements of X also belong to B, so X⊆B. Therefore X∈P(B). This proves P(A)⊆P(B), making option A always true. Equality occurs only in special cases, such as A=B.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
