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

If A = {x ∈ R : x² + 4 = 0} and B = ∅, which statement is correct?

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Answer and explanation

Correct answer: A = B

Because x is restricted to real numbers, x² is always non-negative. Consequently, x² + 4 is always at least 4 and can never equal zero. Thus the equation has no real solution, so A contains no elements and A = ∅. Since B is also given as the empty set, A and B are equal. Option A is therefore correct.

Tags

setsempty setreal numbersequal setsquadratic equationThe Empty SetFinite and Infinite Setsthe empty set finite and infinite sets equal setsMathematics

Frequently asked questions

What is the correct answer to this question?

A = B

Why is this the correct answer?

Because x is restricted to real numbers, x² is always non-negative. Consequently, x² + 4 is always at least 4 and can never equal zero. Thus the equation has no real solution, so A contains no elements and A = ∅. Since B is also given as the empty set, A and B are equal. Option A is therefore 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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