Question

Write each of the following sets in set-builder notation. $$ \\{\ldots,-6,-3,0,3,6,9,12,15, \ldots\\} $$

Short answer

The set {…,-6,-3,0,3,6,9,12,15,…} can be written in set-builder notation as {3n | n ∈ Z}

Step-by-step solution

Identify the pattern

The given set is {…,-6,-3,0,3,6,9,12,15,…}. Observe the numbers and we can see that each term can be obtained by adding 3 to the previous term. This indicates that the numbers are multiples of 3.

Formulate the set-builder notation

Since all terms are multiples of 3, we can represent them as 3n, where n is an integer. So in set-builder notation, the given set can be represented as {3n | n ∈ Z}. Here '|' reads as 'such that' and 'Z' represents the set of all integers.