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Class 10MathematicsSetsThe Empty Set, Finite and Infinite Sets, Equal SetsEasyLevel 10

Which statement is correct for the set A = {x ∈ ℝ : x = x + 1}?

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Answer and explanation

Correct answer: It is the empty set

Subtracting x from both sides of x = x + 1 gives 0 = 1. This is a contradiction and cannot be true for any real number x. Therefore no real number satisfies the defining condition of A. A set containing no elements is called the empty set, written as ∅. Hence A = ∅ and option C is correct.

Tags

setsempty-setcontradictionThe Empty SetFinite and Infinite SetsEqual Setsthe empty set finite and infinite sets equal setsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

It is the empty set

Why is this the correct answer?

Subtracting x from both sides of x = x + 1 gives 0 = 1. This is a contradiction and cannot be true for any real number x. Therefore no real number satisfies the defining condition of A. A set containing no elements is called the empty set, written as ∅. Hence A = ∅ and option C 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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