If P(A) = {∅, {x}}, what is A?
Answer and explanation
Correct answer: {x}
The power set of A contains every subset of A, including the empty set and A itself. The given power set has exactly two elements: ∅ and {x}. Since the non-empty member must be A itself, A = {x}. This also agrees with |P(A)| = 2^|A|: because |P(A)| = 2, we get |A| = 1. Notice that {∅} would produce a different power set, namely {∅, {∅}}.
Frequently asked questions
What is the correct answer to this question?
{x}
Why is this the correct answer?
The power set of A contains every subset of A, including the empty set and A itself. The given power set has exactly two elements: ∅ and {x}. Since the non-empty member must be A itself, A = {x}. This also agrees with |P(A)| = 2^|A|: because |P(A)| = 2, we get |A| = 1. Notice that {∅} would produce a different power set, namely {∅, {∅}}.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
