Which is the most accurate set-builder form for D = {2, 4, 8, 16, 32}?
Answer and explanation
Correct answer: D = {x : x = 2ⁿ, n ∈ ℕ, 1 ≤ n ≤ 5}
Each listed element is a power of 2: 2 = 2¹, 4 = 2², 8 = 2³, 16 = 2⁴ and 32 = 2⁵. Therefore, x = 2ⁿ with n taking the natural-number values from 1 through 5 describes exactly the given five elements. Option D is too broad because it includes 2⁶, 2⁷ and infinitely many more values. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
D = {x : x = 2ⁿ, n ∈ ℕ, 1 ≤ n ≤ 5}
Why is this the correct answer?
Each listed element is a power of 2: 2 = 2¹, 4 = 2², 8 = 2³, 16 = 2⁴ and 32 = 2⁵. Therefore, x = 2ⁿ with n taking the natural-number values from 1 through 5 describes exactly the given five elements. Option D is too broad because it includes 2⁶, 2⁷ and infinitely many more values. Hence option A is correct.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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