If A = {1, {2}}, which must be in P(A)?
Answer and explanation
Correct answer: {{2}}
The elements of A are 1 and the set {2}; the number 2 itself is not an element of A. Every subset of A belongs to P(A). Since {2} is an element of A, the singleton set whose only element is {2}, written {{2}}, is a subset of A and therefore belongs to P(A). Option A is an element of A, not necessarily a subset, while option C is not even an element of A.
Frequently asked questions
What is the correct answer to this question?
{{2}}
Why is this the correct answer?
The elements of A are 1 and the set {2}; the number 2 itself is not an element of A. Every subset of A belongs to P(A). Since {2} is an element of A, the singleton set whose only element is {2}, written {{2}}, is a subset of A and therefore belongs to P(A). Option A is an element of A, not necessarily a subset, while option C is not even an element of A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
