Which statement about ∅ and {∅} is correct?
Answer and explanation
Correct answer: ∅ is empty, but {∅} is a singleton
The empty set, written ∅, has no elements, so its cardinality is 0. In contrast, {∅} is a set whose single element is the empty set itself; therefore, its cardinality is 1 and it is a singleton. The braces create a new set and do not leave the set empty. Hence option C is correct; A and B confuse an element with a set, while D is false.
Frequently asked questions
What is the correct answer to this question?
∅ is empty, but {∅} is a singleton
Why is this the correct answer?
The empty set, written ∅, has no elements, so its cardinality is 0. In contrast, {∅} is a set whose single element is the empty set itself; therefore, its cardinality is 1 and it is a singleton. The braces create a new set and do not leave the set empty. Hence option C is correct; A and B confuse an element with a set, while D is false.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
