If A = {∅, {∅}}, how many subsets does A have?
Answer and explanation
Correct answer: 4
Although the symbols are related, ∅ and {∅} are different objects. The first is the empty set, containing no elements; the second is a singleton set whose only element is ∅. Thus A has exactly two distinct elements: ∅ and {∅}. A set with two elements has 2² = 4 subsets: ∅, {∅}, {{∅}}, and {∅, {∅}}. Therefore option C is correct.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
Although the symbols are related, ∅ and {∅} are different objects. The first is the empty set, containing no elements; the second is a singleton set whose only element is ∅. Thus A has exactly two distinct elements: ∅ and {∅}. A set with two elements has 2² = 4 subsets: ∅, {∅}, {{∅}}, and {∅, {∅}}. Therefore option C is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
