Which option gives the correct set-builder form of P = {2, 4, 8, 16, 32}?
Answer and explanation
Correct answer: P = {x : x = 2ⁿ, n ∈ N, 1 ≤ n ≤ 5}
The governing concept is set-builder notation, which describes a common rule and the allowed values of a variable. The elements are successive powers 2¹, 2², 2³, 2⁴ and 2⁵, so x=2ⁿ with n∈N and 1≤n≤5 gives exactly P. Option B gives multiples of 2, C gives squares, and D includes 2⁰=1 while omitting 32. Hence A is correct.
Frequently asked questions
What is the correct answer to this question?
P = {x : x = 2ⁿ, n ∈ N, 1 ≤ n ≤ 5}
Why is this the correct answer?
The governing concept is set-builder notation, which describes a common rule and the allowed values of a variable. The elements are successive powers 2¹, 2², 2³, 2⁴ and 2⁵, so x=2ⁿ with n∈N and 1≤n≤5 gives exactly P. Option B gives multiples of 2, C gives squares, and D includes 2⁰=1 while omitting 32. Hence A is correct.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: General chapter practice.
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