If A = {∅, {2}, 2}, which of the following statements is correct?
Answer and explanation
Correct answer: Both {2} ∈ A and {2} ⊂ A are true
The set A has three distinct elements: the empty set ∅, the singleton set {2}, and the number 2. Since {2} is explicitly listed, {2} ∈ A is true. Also, the only element of {2} is 2, and 2 is explicitly in A; therefore {2} is a proper subset of A, so {2} ⊂ A is true. Hence option A is correct. Notice that 2 and {2} are different objects.
Frequently asked questions
What is the correct answer to this question?
Both {2} ∈ A and {2} ⊂ A are true
Why is this the correct answer?
The set A has three distinct elements: the empty set ∅, the singleton set {2}, and the number 2. Since {2} is explicitly listed, {2} ∈ A is true. Also, the only element of {2} is 2, and 2 is explicitly in A; therefore {2} is a proper subset of A, so {2} ⊂ A is true. Hence option A is correct. Notice that 2 and {2} are different objects.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
