What is A = {x ∈ ℕ : x is a perfect cube less than 30}?
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Answer and explanation
Correct answer: A = {1, 8, 27}
The positive natural-number cubes are obtained as 1³ = 1, 2³ = 8, 3³ = 27, and 4³ = 64. The condition requires the cube to be less than 30, so 1, 8, and 27 are included, while 64 is excluded. Under the usual school convention that ℕ begins with 1, zero is not included. Therefore A = {1, 8, 27}.
Frequently asked questions
What is the correct answer to this question?
A = {1, 8, 27}
Why is this the correct answer?
The positive natural-number cubes are obtained as 1³ = 1, 2³ = 8, 3³ = 27, and 4³ = 64. The condition requires the cube to be less than 30, so 1, 8, and 27 are included, while 64 is excluded. Under the usual school convention that ℕ begins with 1, zero is not included. Therefore A = {1, 8, 27}.
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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