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Class 10MathematicsSetsThe Empty Set, Finite and Infinite Sets, Equal SetsMediumLevel 4

If D = {x : x ∈ ℕ, x² + 2x + 1 = 0}, what type of set is D?

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Answer and explanation

Correct answer: Empty set

The equation x² + 2x + 1 = 0 is (x + 1)² = 0, so its only algebraic solution is x = -1. However, the set definition requires x to be a natural number. Since -1 is not a natural number, it is rejected and no permitted element remains. Thus D contains no elements and is the empty set, written as ∅.

Tags

setsempty setnatural numbersquadratic equationThe 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?

Empty set

Why is this the correct answer?

The equation x² + 2x + 1 = 0 is (x + 1)² = 0, so its only algebraic solution is x = -1. However, the set definition requires x to be a natural number. Since -1 is not a natural number, it is rejected and no permitted element remains. Thus D contains no elements and is the empty set, written as ∅.

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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