Answer: [tex]B=\{3^x:x\in N, x\leq4\}[/tex]
Step-by-step explanation:
Given set: [tex]B=\{3,9,27,81\}[/tex] which is in a rooster form.
A set-builder form is a mathematical form to representing a set by stating the properties that its elements must satisfy.
In the given set each element is a multiple of 3.
[tex]3=3^1\\9=3^2\\27=3^3\\81=3^4[/tex]
So, [tex]B=\{3^1, 3^2, 3^3, 3^4\}[/tex] ,where 1,2,3,4 are natural numbers
The set-builder notation would be :
[tex]B=\{3^x:x\in N, x\leq4\}[/tex], where N is the set of natural numbers.
