If A = {1,{2}}, which of the following is an element of P(A)?
Answer and explanation
Correct answer: {{2}}
The set A has exactly two elements: the number 1 and the set {2}. An element of P(A) must be a subset of A, so all of its elements must be either 1 or {2}. The set {{2}} has the single element {2}, which belongs to A; therefore {{2}} ⊆ A and {{2}} ∈ P(A). In contrast, {2} contains the number 2, which is not an element of A, and {1,2} also contains 2. Thus option B is correct.
Frequently asked questions
What is the correct answer to this question?
{{2}}
Why is this the correct answer?
The set A has exactly two elements: the number 1 and the set {2}. An element of P(A) must be a subset of A, so all of its elements must be either 1 or {2}. The set {{2}} has the single element {2}, which belongs to A; therefore {{2}} ⊆ A and {{2}} ∈ P(A). In contrast, {2} contains the number 2, which is not an element of A, and {1,2} also contains 2. Thus option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
