If A = {1, 2, {3}}, which of the following statements is correct?
Answer and explanation
Correct answer: {3} ∈ A
The set A has exactly three elements: 1, 2, and the set {3}. The number 3 itself is not directly listed as an element of A; instead, the one-element set {3} is listed. Therefore, {3} ∈ A is true. Statement A is false because 3 ∉ A. Statement C is false because {1, 2, 3} has 3 as an element, whereas A has {3} as an element. Statement D is also false because {3} ⊂ A would require its element 3 to belong to A. Always distinguish membership (∈) from subset notation (⊂).
Frequently asked questions
What is the correct answer to this question?
{3} ∈ A
Why is this the correct answer?
The set A has exactly three elements: 1, 2, and the set {3}. The number 3 itself is not directly listed as an element of A; instead, the one-element set {3} is listed. Therefore, {3} ∈ A is true. Statement A is false because 3 ∉ A. Statement C is false because {1, 2, 3} has 3 as an element, whereas A has {3} as an element. Statement D is also false because {3} ⊂ A would require its element 3 to belong to A. Always distinguish membership (∈) from subset notation (⊂).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
