What is the correct identification of A = {x ∈ N : 2x + 1 = 2x}?
Answer and explanation
Correct answer: Empty set
The condition 2x + 1 = 2x can be simplified by subtracting 2x from both sides, giving 1 = 0. This statement is impossible and is independent of the value of x. Therefore no natural number satisfies the defining condition of A. A set containing no elements is called the empty set, denoted by ∅. Hence option B is correct; it is not a singleton, a two-element set, or an infinite set.
Frequently asked questions
What is the correct answer to this question?
Empty set
Why is this the correct answer?
The condition 2x + 1 = 2x can be simplified by subtracting 2x from both sides, giving 1 = 0. This statement is impossible and is independent of the value of x. Therefore no natural number satisfies the defining condition of A. A set containing no elements is called the empty set, denoted by ∅. Hence option B is correct; it is not a singleton, a two-element set, or an infinite set.
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.
