Let's tackle each part of the problem based on the provided image:

Part (a):

• Roster form is given as: $\{2, 3, 4, 5, \dots\}$.

• We need to write the Set-builder form.

  The pattern in the roster form shows that the elements of the set start from 2 and increase by 1 indefinitely. We can describe this set in set-builder notation as:

  $\{x \mid x \geq 2 \text{ and } x \in \mathbb{Z}\}$ This means the set contains integers ($x \in \mathbb{Z}$) starting from 2 and going upwards.

Part (b):

• Set-builder form is given as: $\{y \mid y \text{ is an integer and } -2 \leq y \leq 1\}$.

• We need to convert this into Roster form.

  The integers between $-2$ and $1$ are: $\{-2, -1, 0, 1\}$.

Thus, the answers are:

1. (a) Set-builder form: $\{x \mid x \geq 2 \text{ and } x \in \mathbb{Z}\}$
2. (b) Roster form: $\{-2, -1, 0, 1\}$

Do you need further clarifications or details on these conversions?

Here are some follow-up questions:

1. Can you explain how set-builder notation differs from roster form?
2. How would you describe a set that includes only even numbers greater than 10 using set-builder form?
3. What is the difference between natural numbers and integers in set notation?
4. Can a set in roster form always be written in set-builder form?
5. How would you represent the set of all integers less than 0 in roster form?

Tip: When writing sets in set-builder notation, always carefully define the conditions that describe all elements in the set.