If P(A) = {∅, {p}, {q}, {p,q}}, what is A?
Answer and explanation
Correct answer: {p, q}
For any finite set A, the original set A is itself one of the members of its power set. In the given collection, {p,q} is the largest subset and contains both elements that occur in the singleton subsets {p} and {q}. Therefore the original set must be A = {p,q}. Notice that ∅ is a subset, not the original set here, and {{p},{q}} has different elements from A.
Frequently asked questions
What is the correct answer to this question?
{p, q}
Why is this the correct answer?
For any finite set A, the original set A is itself one of the members of its power set. In the given collection, {p,q} is the largest subset and contains both elements that occur in the singleton subsets {p} and {q}. Therefore the original set must be A = {p,q}. Notice that ∅ is a subset, not the original set here, and {{p},{q}} has different elements from A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
