Which statement is always true for any set A?
Answer and explanation
Correct answer: ∅ ∈ P(A)
The empty set is a subset of every set, including A. By definition, P(A) is the set of all subsets of A. Therefore ∅ is always an element of P(A), so option C is universally true. Options A and B are not necessary because A may not contain itself and may not contain the empty set. Option D is not guaranteed because U need not be a subset of A.
Frequently asked questions
What is the correct answer to this question?
∅ ∈ P(A)
Why is this the correct answer?
The empty set is a subset of every set, including A. By definition, P(A) is the set of all subsets of A. Therefore ∅ is always an element of P(A), so option C is universally true. Options A and B are not necessary because A may not contain itself and may not contain the empty set. Option D is not guaranteed because U need not be a subset of A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
