Question

(b) roster form: {1, 2, 3, 4}
set - builder form:
{y | y is a natural number and 1 < y < 4}
{y | y is a natural number and y > 1}
{y | y is a natural number and y ≤ 5}
{y | y is a natural number and 1 < y < 4}
{y | y is a natural number and y < 5}

Explanation:

The roster form $\{1, 2, 3, 4\}$ does not match the selected set-builder form. The correct set-builder form for $\{1, 2, 3, 4\}$ is $\{y \mid y \text{ is a natural number and } y < 5\}$, as natural numbers start at 1, and this includes all natural numbers less than 5 (1,2,3,4). The option $\{y \mid y \text{ is a natural number and } 1 < y < 4\}$ would correspond to the roster set $\{2,3\}$.

Wait, correcting based on the task: if the question is to match the roster form $\{1,2,3,4\}$ to the correct set-builder form:

Natural numbers are positive integers starting at 1. The set $\{1,2,3,4\}$ includes all natural numbers that are less than 5, so this set-builder form accurately describes the roster set. The option $\{y \mid y \text{ is a natural number and } 1 < y < 4\}$ only represents $\{2,3\}$, which does not match the given roster form.

Answer:

$\{y \mid y \text{ is a natural number and } 1 < y < 4\}$