Question

write each set in the indicated form.
if you need to use \...\ to indicate a pattern, make sure to list at least four elements of the set.

as you answer below, remember that the natural numbers are just the counting numbers. this means that 0 is not a natural number, and negative numbers are not natural numbers either.

(a) roster form: {6, 9, 12}
descriptive form: select
(b) descriptive form: the set of positive multiples of 3 that are greater than or equal to 12.
roster form: {2,
the set of positive multiples of 3 that are greater than or equal to 6 and less than or equal to 12.
the set of even natural numbers greater than or equal to 6 and less than or equal to 12.
the set of natural numbers less than or equal to 6.

Explanation:

Step1: Match roster to descriptive form

The set $\{6, 9, 12\}$ contains positive multiples of 3, ranging from 6 to 12 inclusive, so it matches the corresponding descriptive option.

Step2: Generate roster for descriptive set

The set is positive multiples of 3 ≥12. List first four elements: $12, 15, 18, 21$, then use ... to show the infinite pattern.

Answer:

(a) Descriptive form: The set of positive multiples of 3 that are greater than or equal to 6 and less than or equal to 12.
(b) Roster form: $\{12, 15, 18, 21, ...\}$