The problem asks us to choose the correct set of integers $y$ such that $y \geq -7$.

Analysis:

1. The condition given is $y \geq -7$, meaning $y$ must be greater than or equal to $-7$.
2. $y$ is an integer, so it includes all integer values starting from $-7$ and increasing.

Checking the options:

1. Option 1: $\{7, 8, 9, 10, \ldots\}$
   This set starts at 7, but it doesn't include $-7$ or any values below 7, so it doesn't satisfy the condition.

2. Option 2: $\{\ldots, -11, -10, -9, -8, -7\}$
   This set includes $-7$ but also includes numbers less than $-7$, which doesn't meet the requirement $y \geq -7$.

3. Option 3: $\{-6, -5, -4, -3, \ldots\}$
   This set starts at $-6$ and continues with values greater than $-7$. It includes $-6$, so it satisfies the condition $y \geq -7$.

4. Option 4: $\{-7, -6, -5, -4, \ldots\}$
   This set starts at $-7$ and includes all integers greater than or equal to $-7$, which is exactly what is required.

5. Option 5: $\{\ldots, -3, -4, -5, -6\}$
   This set includes only negative values less than or equal to $-3$, which does not meet the condition $y \geq -7$.

Correct Answer:

Option 4: $\{-7, -6, -5, -4, \ldots\}$

Would you like further details or have any questions?

Here are some related questions for further practice:

1. What is the set of integers $y$ such that $y < 5$?
2. How would you represent the set of all positive integers greater than 10?
3. What does the set notation $\{ x : x \text{ is an integer and } x \leq 0 \}$ represent?
4. What is the interval notation for $y \geq -7$?
5. Can the set $\{ -10, -9, -8, \ldots \}$ satisfy $y > -7$?

Tip: Always carefully compare each option against the given condition to identify the correct set.