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Class 10MathematicsSetsPower Set and SubsetsMediumLevel 8

If A = {x ∈ R : x² + 1 = 0}, what is A as a subset of the real numbers?

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Answer and explanation

Correct answer: ∅

For every real number x, x² is non-negative, so x² + 1 is at least 1 and can never equal zero. Consequently, the defining condition has no real solution, and A contains no elements. Therefore A is the empty set ∅. The values i and −i solve the equation only in the complex number system, not in R.

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setsempty_setreal_numberscomplex_numbersPower Set and SubsetsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

∅

Why is this the correct answer?

For every real number x, x² is non-negative, so x² + 1 is at least 1 and can never equal zero. Consequently, the defining condition has no real solution, and A contains no elements. Therefore A is the empty set ∅. The values i and −i solve the equation only in the complex number system, not in R.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.

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