Which of the following is a member of the power set P(∅)?
Answer and explanation
Correct answer: ∅
The empty set has no elements, so its only subset is the empty set itself. Therefore P(∅) = {∅}. The notation is important: ∅ is the sole member of the power set, whereas {∅} is the power set as a whole, not a member of that power set. The number 0 and the singleton {0} are not subsets of ∅ because 0 is not an element of ∅.
Frequently asked questions
What is the correct answer to this question?
∅
Why is this the correct answer?
The empty set has no elements, so its only subset is the empty set itself. Therefore P(∅) = {∅}. The notation is important: ∅ is the sole member of the power set, whereas {∅} is the power set as a whole, not a member of that power set. The number 0 and the singleton {0} are not subsets of ∅ because 0 is not an element of ∅.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
