Which option gives the correct set-builder form of P={3,9,27,81}?
Answer and explanation
Correct answer: P={x:x=3^n, n∈N, 1≤n≤4}
The governing concept is set-builder notation: a rule must generate every listed member and no extra member. Here 3=3¹, 9=3², 27=3³, and 81=3⁴, so x=3^n with n∈N and 1≤n≤4 describes exactly P. Option B gives multiples of 3, C gives cubes of n, and D gives multiples of 9, so none matches the set.
Frequently asked questions
What is the correct answer to this question?
P={x:x=3^n, n∈N, 1≤n≤4}
Why is this the correct answer?
The governing concept is set-builder notation: a rule must generate every listed member and no extra member. Here 3=3¹, 9=3², 27=3³, and 81=3⁴, so x=3^n with n∈N and 1≤n≤4 describes exactly P. Option B gives multiples of 3, C gives cubes of n, and D gives multiples of 9, so none matches the set.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems.
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