If J₁ = {x : x ∈ ℕ and x is a perfect cube less than 100}, what are the elements of J₁?
Answer and explanation
Correct answer: J₁ = {1, 8, 27, 64}
The natural-number cubes less than 100 are obtained from 1³, 2³, 3³, and 4³. Their values are 1, 8, 27, and 64. The next cube is 5³ = 125, which is greater than 100 and must be excluded. Therefore J₁ = {1, 8, 27, 64}. The set is finite because only finitely many natural numbers have cubes below 100.
Frequently asked questions
What is the correct answer to this question?
J₁ = {1, 8, 27, 64}
Why is this the correct answer?
The natural-number cubes less than 100 are obtained from 1³, 2³, 3³, and 4³. Their values are 1, 8, 27, and 64. The next cube is 5³ = 125, which is greater than 100 and must be excluded. Therefore J₁ = {1, 8, 27, 64}. The set is finite because only finitely many natural numbers have cubes below 100.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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