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: {1, 2, 3, 4}
descriptive form: select
(b) descriptive form: the set of natural numbers less than or equal to 4.
roster form:

the set of natural numbers less than or equal to 4.
the set of positive multiples of 4 that are greater than or equal to 8 and less than or equal to 16.
the set of natural numbers greater than or equal to 4.
the set of even natural numbers.

Explanation:

Step1: Match roster to description

The roster $\{1,2,3,4\}$ includes all natural numbers from 1 to 4, so it matches "The set of natural numbers less than or equal to 4."

Step2: Find multiples for roster

Positive multiples of 4 between 8 and 16 (inclusive) are $4\times2=8$, $4\times3=12$, $4\times4=16$. Compile into roster form: $\{8, 12, 16\}$

Answer:

(a) Descriptive form: The set of natural numbers less than or equal to 4.
(b) Roster form: $\{8, 12, 16\}$