What is the set A = {x ∈ ℕ : x is a solution of x + 2 = x}?
Answer and explanation
Correct answer: ∅
Subtracting x from both sides of x + 2 = x gives 2 = 0. This is a contradiction, because 2 is not equal to 0. Consequently, no number—natural or otherwise—can satisfy the equation. The solution set therefore contains no elements, so it is the empty set, denoted by ∅. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
∅
Why is this the correct answer?
Subtracting x from both sides of x + 2 = x gives 2 = 0. This is a contradiction, because 2 is not equal to 0. Consequently, no number—natural or otherwise—can satisfy the equation. The solution set therefore contains no elements, so it is the empty set, denoted by ∅. Hence option A is correct.
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.
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