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

Let A = {x ∈ ℤ : x is a power of 2 and x < 0}. What is A?

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Answer and explanation

Correct answer: A = ∅

Every integral power of 2 is positive: for any integer n, 2ⁿ > 0, including negative exponents such as 2⁻¹ = 1/2. Therefore no power of 2 can satisfy x < 0. Since the set contains no element, it is the empty set, written as ∅. The negative numbers listed in option B are not powers of positive 2.

Tags

setsempty setpowers of 2integersThe 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?

Every integral power of 2 is positive: for any integer n, 2ⁿ > 0, including negative exponents such as 2⁻¹ = 1/2. Therefore no power of 2 can satisfy x < 0. Since the set contains no element, it is the empty set, written as ∅. The negative numbers listed in option B are not powers of positive 2.

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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