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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.

Choose the correct elements in the set for the following: {y : y is an integer and y ≥ -1}.

Learn how to determine the correct subset of integers where y ≥ -1. This problem involves set theory and inequalities, perfect for students in Grades 6-8. Understand the process of selecting the appropriate set from multiple options.

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