Question

Write the set E = {3, 6, 9, 12, 15, 18} in the set builder form.

Answer 1

Hint: In order to solve this question, we need to know that whenever we are given any set in the roster form and we have to convert it into set builder form, then we have to follow a basic step, which is to find a relation between all the elements of the set.

Complete step-by-step answer:
In the given question, we have been asked to write set E = {3, 6, 9, 12, 15, 18} in the set-builder form. Now, we know that whenever we have to convert any set in the rooster form to set builder form, then we need to identify a common relation among each term of the set. So, we will find the same in this question. We have been given E = {3, 6, 9, 12, 15, 18}. Now, we will consider each of the elements of the set one by one. So, we can write them as,
$\begin{align}
  & 3=3\times 1 \\
 & 6=3\times 2 \\
 & 9=3\times 3 \\
 & 12=3\times 4 \\
 & 15=3\times 5 \\
 & 18=3\times 6 \\
\end{align}$
Now, we can see here, that there is a common thing among the elements of set E, that is, all of them are multiples of 3. So, we can write x = 3n. Also, we can see that the value of n is varying from 1 to 6. So, we can write the range of n as $1\le n\le 6$.
Hence, we can represent the set E as $\left\{ x:x=3n,1\le n\le 6 \right\}$.

Note: While solving such types of questions, we need to remember that we have to always look for a relation between all the terms. Also, we have to remember that the set builder form is of the type, {f(x): some relation, range}.