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

If A = {1, 2, 3} and B = {x ∈ ℕ : x³ ≤ 27}, which statement is correct?

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Answer and explanation

Correct answer: A = B

For natural numbers, test the values around the boundary: 1³ = 1, 2³ = 8, and 3³ = 27, so 1, 2, and 3 satisfy x³ ≤ 27. The next natural number does not, because 4³ = 64 > 27. Therefore B = {1, 2, 3}, which is exactly the same collection of elements as A. Hence A = B; both sets are finite and equal.

Tags

setsequal-setscube-inequalityfinite-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?

A = B

Why is this the correct answer?

For natural numbers, test the values around the boundary: 1³ = 1, 2³ = 8, and 3³ = 27, so 1, 2, and 3 satisfy x³ ≤ 27. The next natural number does not, because 4³ = 64 > 27. Therefore B = {1, 2, 3}, which is exactly the same collection of elements as A. Hence A = B; both sets are finite and equal.

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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