If A = {∅, {∅}, 0}, what is n(P(A))?
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Answer and explanation
Correct answer: 8
The three listed objects are distinct elements: ∅ is the empty set, {∅} is a one-element set whose element is ∅, and 0 is a number. Since A has 3 distinct elements, the number of its subsets is 2^3 = 8. Therefore n(P(A)) = 8. It is important not to confuse ∅ with {∅}; they are different sets.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The three listed objects are distinct elements: ∅ is the empty set, {∅} is a one-element set whose element is ∅, and 0 is a number. Since A has 3 distinct elements, the number of its subsets is 2^3 = 8. Therefore n(P(A)) = 8. It is important not to confuse ∅ with {∅}; they are different sets.
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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