If A = {∅}, which of the following statements is true?
Answer and explanation
Correct answer: ∅ ∈ A
The notation A = {∅} means that A is a set whose only element is the empty set. Therefore, ∅ ∈ A is true. However, A is not itself empty: it has one element. Hence ∅ = A is false, and A ∈ ∅ is impossible because the empty set contains no elements. This example shows the essential difference between ∅, which has zero elements, and {∅}, which has one element.
Frequently asked questions
What is the correct answer to this question?
∅ ∈ A
Why is this the correct answer?
The notation A = {∅} means that A is a set whose only element is the empty set. Therefore, ∅ ∈ A is true. However, A is not itself empty: it has one element. Hence ∅ = A is false, and A ∈ ∅ is impossible because the empty set contains no elements. This example shows the essential difference between ∅, which has zero elements, and {∅}, which has one element.
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.
