Let's solve the two parts of the problem shown in the image:

(a) Convert Roster Form to Set-Builder Form:

Given Roster form:
$\{-1, 0, 1, 2, 3\}$

We need to convert it to Set-Builder form.

Solution:

• This is a small set with consecutive integers from $-1$ to $3$.
• In set-builder notation, it can be written as:

$\{x \mid x \in \mathbb{Z}, -1 \leq x \leq 3\}$

Explanation:

• $\mid$ means "such that."
• $x \in \mathbb{Z}$ ensures that only integers are included.
• The condition $-1 \leq x \leq 3$ restricts the integers to the given range.

(b) Convert Set-Builder Form to Roster Form:

Given Set-Builder form:
$\{y \mid y \text{ is an integer and } y \geq -3\}$

Solution:

• The set contains all integers greater than or equal to $-3$.
• In Roster form, this set starts from $-3$ and continues indefinitely. Listing the first few elements:

$\{-3, -2, -1, 0, 1, 2, \dots\}$

If you have further questions or need more details, let me know!

5 Related Questions:

1. What is the difference between roster form and set-builder form?
2. How do you write infinite sets in roster form?
3. How can you convert inequalities involving integers into set-builder notation?
4. Can set-builder notation express sets with only specific conditions (like odd numbers)?
5. How do you denote sets of non-integers in set-builder notation?

Tip:
In set-builder notation, always include the type of elements (like integers or real numbers) to avoid ambiguity.