If A = {5}, what is P(A)?
Answer and explanation
Correct answer: {∅, {5}}
The power set P(A) is the set containing every subset of A. For the singleton set A = {5}, the only subsets are the empty set ∅ and the set A itself, {5}. Therefore, P(A) = {∅, {5}}. Notice the difference between the number 5 and the set {5}: the power set contains subsets as its elements, so {5}, not 5, appears inside it. Hence option D is correct.
Frequently asked questions
What is the correct answer to this question?
{∅, {5}}
Why is this the correct answer?
The power set P(A) is the set containing every subset of A. For the singleton set A = {5}, the only subsets are the empty set ∅ and the set A itself, {5}. Therefore, P(A) = {∅, {5}}. Notice the difference between the number 5 and the set {5}: the power set contains subsets as its elements, so {5}, not 5, appears inside it. Hence option D is correct.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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