If D₁ = {x : x ∈ ℤ, 2 < x² ≤ 16}, what is the roster form of D₁?
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Answer and explanation
Correct answer: D₁ = {−4, −3, −2, 2, 3, 4}
We need integers satisfying both inequalities. The condition x² ≤ 16 gives −4 ≤ x ≤ 4. The condition 2 < x² excludes 0 and ±1, because their squares are 0 and 1. The integers remaining in the interval are ±2, ±3, and ±4. Hence the roster form is {−4, −3, −2, 2, 3, 4}, which is option A.
Frequently asked questions
What is the correct answer to this question?
D₁ = {−4, −3, −2, 2, 3, 4}
Why is this the correct answer?
We need integers satisfying both inequalities. The condition x² ≤ 16 gives −4 ≤ x ≤ 4. The condition 2 < x² excludes 0 and ±1, because their squares are 0 and 1. The integers remaining in the interval are ±2, ±3, and ±4. Hence the roster form is {−4, −3, −2, 2, 3, 4}, which is option A.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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