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Class 10MathematicsSetsThe Empty Set, Finite and Infinite Sets, Equal SetsEasyLevel 6

If A = {x : x ∈ ℕ and x is a square root of 16}, what is A?

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Answer and explanation

Correct answer: {4}

The numbers whose square is 16 are 4 and −4, because 4² = 16 and (−4)² = 16. However, the condition specifies that x belongs to ℕ, the set of natural numbers. Under the usual school convention, −4 is not a natural number, so it must be excluded. Therefore the only member of A is 4, and A = {4}.

Tags

setsnatural-numberssquare-rootsfinite-setThe 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?

{4}

Why is this the correct answer?

The numbers whose square is 16 are 4 and −4, because 4² = 16 and (−4)² = 16. However, the condition specifies that x belongs to ℕ, the set of natural numbers. Under the usual school convention, −4 is not a natural number, so it must be excluded. Therefore the only member of A is 4, and A = {4}.

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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