If A = ∅, which statement about P(A) is correct?
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Answer and explanation
Correct answer: P(A) = {∅}
The empty set has no elements, but it does have one subset: itself. Therefore the power set of the empty set contains exactly one element, namely the empty set: P(∅) = {∅}. It is important to distinguish ∅ from {∅}; the former has zero elements, while the latter has one element. Thus option B is correct.
Frequently asked questions
What is the correct answer to this question?
P(A) = {∅}
Why is this the correct answer?
The empty set has no elements, but it does have one subset: itself. Therefore the power set of the empty set contains exactly one element, namely the empty set: P(∅) = {∅}. It is important to distinguish ∅ from {∅}; the former has zero elements, while the latter has one element. Thus option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
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