Question

Write the given set in the set-builder form: {5, 25, 125, 625}

Answer 1

there are two methods to represent a set.
(1) set - builder form and (2) roaster form.

$\textbf{set-builder form}$ : when the collection of objects of a set is represented by using its properties is known as set builder form. for example : A = {1,2, 3, 4, 5} is given then we can write A in set builder form of A = {x : x is a natural number less than 6}.

here, Let A = {5, 25, 125, 625}
we observed that , 5 = 5¹ , 25 = 5², 125 = 5³
625 = 5⁴
so, we can write A in set - builder form,
A = {x : x = 5ⁿ , n$\in$N and 1 ≤ n ≤ 4}

Answer 2

Answer:

{ 5ⁿ : n € N , n ≤ 4 }

Step-by-step explanation:

{ 5 , 25 , 125 , 625 }

= { 5¹ , 5² , 5³ , 5⁴ }

Set builder form :

{ 5ⁿ : n € N , n ≤ 4 }

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