Question

write each set in the indicated form.
if you need to use \...\ to indicate a pattern, make sure to list at least the first four elements of the set.
(a) set - builder form: {x | x is a natural number and x > 5}
roster form: {6, 7, 8, 9,...}
(b) roster form: {15, 16, 17}
set - builder form: select
{y | y is a natural number and y ≥ 15}
{y | y is a natural number and 15 < y < 17}
{y | y is a natural number and 15 ≤ y ≤ 17}
{y | y is a natural number and y < 17}

Explanation:

Step1: Analyze roster set elements

The roster form is $\{15, 16, 17\}$, which includes natural numbers starting at 15, ending at 17, and all values in between.

Step2: Match to set-builder condition

We need a condition that includes $15$, $16$, $17$. The inequality $15 \leq y \leq 17$ (for natural numbers $y$) exactly describes these values.

Answer:

$\{y \mid y \text{ is a natural number and } 15 \leq y \leq 17\}$