The question asks you to choose the correct elements in the set described as:

$\{ y : y \text{ is an integer and } y \geq -1 \}$

This set includes all integers $y$ such that $y \geq -1$. Let's analyze the possible options:

• $\{3, 4, 5, 6, \dots\}$: This set starts from 3, so it is not correct since $y \geq -1$ includes smaller integers like $-1, 0, 1, 2$.

• $\{2, 3, 4, 5, 6, \dots\}$: This set starts from 2, which excludes numbers like $-1$ and $0$, so it's also incorrect.

• $\{-1, 0, 1, 2, 3, \dots\}$: This set starts from $-1$ and includes all integers greater than or equal to $-1$, which matches the given set. This is the correct answer.

• $\{0, 1, 2, 3, \dots\}$: This set starts from 0, so it misses the number $-1$, making it incorrect.

Thus, the correct answer is:

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

Would you like more details on this explanation? Here are five related questions to explore:

1. What is the difference between roster form and set-builder notation?
2. How do you determine the correct set given a set-builder notation?
3. What other sets could be defined by conditions on integers like $y \geq 0$?
4. How would the set change if the condition were $y \leq 3$?
5. Can a set in roster form always be written in set-builder notation?

Tip: When working with sets, always check the smallest and largest possible values that satisfy the condition.