Let A be the set of all singleton subsets of {a, b, c}, and let B = {{a}, {b}, {c}}. What is the correct relation between A and B?
Answer and explanation
Correct answer: A = B
A singleton subset contains exactly one element. The singleton subsets of {a, b, c} are {a}, {b}, and {c}. Therefore, A = {{a}, {b}, {c}}. This is exactly the given set B, so A and B have the same elements and A = B. Notice that a, b, and c themselves are not the elements of A; the singleton sets {a}, {b}, and {c} are its elements. Thus neither set is a proper subset of the other.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
A singleton subset contains exactly one element. The singleton subsets of {a, b, c} are {a}, {b}, and {c}. Therefore, A = {{a}, {b}, {c}}. This is exactly the given set B, so A and B have the same elements and A = B. Notice that a, b, and c themselves are not the elements of A; the singleton sets {a}, {b}, and {c} are its elements. Thus neither set is a proper subset of the other.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
