Question

Write the following sets in set builder (Rule Method) form:
$B_6=\text{{...., -6, -3, 0, 3, 6, ....}}$

Answer 1

Step: Express the given set in Set builder (Rule Method) form :

In set builder form, the actual elements of the set are not written, but a statement or a formula or a rule is written in briefest possible way to represent the elements of the set.

Given:
$B_6=\text{{...., -6, -3, 0, 3, 6, ....}}$

As, $-6,-3,0,3,6$ are the negative and positive multiples of 3.

Therefore, elements of $B_6$ are in the form of $3n$, where

$n\in Z.$

Hence, set builder form of $B_6$ is

$B_6=\{x:x=3n,n\in Z\}.$