Question

Express the following sets in the set-builder form.

$\{3,6,9,12,15\}$

Answer 1

First recall the the definition of set builder form and then solve the question accordingly.

Set builder form : Set-builder notation is a notation for describing a set by indicating the properties that its members must satisfy.

Let $\mathrm{B}=\{3,6,9,12,15\}$

Thus set builder form is $\mathrm{B}=\left\{\mathrm{x}:\mathrm{x}=3\mathrm{n},\mathrm{where}\mathrm{n}\in \mathrm{N}\mathrm{and}\mathrm{n}\le 5\right\}$

Hence, the set builder form of $\{3,6,9,12,15\}$ is $\left\{x:x=3n,\mathrm{where}n\in N\mathrm{and}n\le 5\right\}$.