If A = ∅, then what is P(A)?
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Answer and explanation
Correct answer: {∅}
The empty set has no elements, but it has exactly one subset: the empty set itself. Therefore, the power set of the empty set contains one member, namely ∅, and is written P(∅) = {∅}. The notation matters: ∅ is the empty set, whereas {∅} is a set containing the empty set as its element. Thus option B is correct.
Frequently asked questions
What is the correct answer to this question?
{∅}
Why is this the correct answer?
The empty set has no elements, but it has exactly one subset: the empty set itself. Therefore, the power set of the empty set contains one member, namely ∅, and is written P(∅) = {∅}. The notation matters: ∅ is the empty set, whereas {∅} is a set containing the empty set as its 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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