If A = {1, {2}, 3}, which statement is true?
Answer and explanation
Correct answer: {2} ∈ A
The set A has exactly three elements: 1, the set {2}, and 3. Therefore {2} is an element of A, so option A is true. However, 2 itself is not an element of A; it is inside the nested set {2}. Options C and D are also false because both require 2 to be an element of A, which it is not. This example shows why membership (∈) and subset (⊆) must be distinguished carefully, especially when a set contains another set as one of its elements.
Frequently asked questions
What is the correct answer to this question?
{2} ∈ A
Why is this the correct answer?
The set A has exactly three elements: 1, the set {2}, and 3. Therefore {2} is an element of A, so option A is true. However, 2 itself is not an element of A; it is inside the nested set {2}. Options C and D are also false because both require 2 to be an element of A, which it is not. This example shows why membership (∈) and subset (⊆) must be distinguished carefully, especially when a set contains another set as one of its elements.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
