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) roster form: {3, 4, 5, 6, …}
set - builder form: select
(b) set - builder form: {x | x is a natural number and 2 < x < 7}
roster form: {1,2 {x | x is a natural number and x ≤ 7}
{x | x is a natural number and x ≥ 3}
{x | x is a natural number and x > 3}

Explanation:

Step1: Analyze part (a) roster form

The roster $\{3, 4, 5, 6, ...\}$ includes all natural numbers greater than 3.

Step2: Match to set-builder form

The correct set-builder notation is $\{x \mid x \text{ is a natural number and } x > 3\}$.

Step3: Analyze part (b) set-builder form

The notation $\{x \mid x \text{ is a natural number and } 2 < x < 7\}$ means natural numbers between 2 and 7 (not including 2 and 7).

Step4: Convert to roster form

The natural numbers satisfying $2 < x < 7$ are 3, 4, 5, 6, so roster form is $\{3, 4, 5, 6\}$.

Answer:

(a) Set-builder form: $\{x \mid x \text{ is a natural number and } x > 3\}$
(b) Roster form: $\{3, 4, 5, 6\}$