If A = {∅, {∅}}, which of the following is an element of P(A)?
Answer and explanation
Correct answer: {{∅}}
The governing definition is P(A) = the set of all subsets of A. Here A has two elements: ∅ and {∅}. The set {{∅}} contains the single element {∅}, which is an element of A; hence {{∅}} is a subset of A and therefore belongs to P(A). Option A is correct. Option B is a membership statement rather than the required subset, and 1 and {1} contain objects unrelated to A, so they are not subsets of A.
Frequently asked questions
What is the correct answer to this question?
{{∅}}
Why is this the correct answer?
The governing definition is P(A) = the set of all subsets of A. Here A has two elements: ∅ and {∅}. The set {{∅}} contains the single element {∅}, which is an element of A; hence {{∅}} is a subset of A and therefore belongs to P(A). Option A is correct. Option B is a membership statement rather than the required subset, and 1 and {1} contain objects unrelated to A, so they are not subsets of A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
