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Class 10MathematicsSetsThe Empty Set, Finite and Infinite Sets, Equal SetsEasyLevel 3

What is the correct statement about A = {x ∈ ℝ : x = x + 1}?

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Answer and explanation

Correct answer: A = ∅

Subtracting x from both sides of the condition x = x + 1 gives 0 = 1. This is a contradiction and cannot be true for any real number x. Consequently, there is no real number belonging to A. A set containing no elements is called the empty set, denoted by ∅, so A = ∅.

Tags

setsempty setcontradictionreal numbersThe 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?

A = ∅

Why is this the correct answer?

Subtracting x from both sides of the condition x = x + 1 gives 0 = 1. This is a contradiction and cannot be true for any real number x. Consequently, there is no real number belonging to A. A set containing no elements is called the empty set, denoted by ∅, so A = ∅.

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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