Question - Writing Sets of Multiples in Roster and Set-Builder Notations

To find all multiples of \(3\) between \(1\) and \(20\), we list the multiples within this range.

Roster form: \(\{3, 6, 9, 12, 15, 18\}\)

To express this set in set-builder notation, we define the properties that all elements of the set share. All elements \(x\) are multiples of \(3\), hence \(x = 3n\) for some integer \(n\), and \(x\) is greater than \(1\) and less than or equal to \(20\).

Set-builder form: \(\{x \mid x = 3n, n \in \mathbb{Z}, 1 < x \leq 20\}\)