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We are given two sets in the problem:

- Set \( A = \{ x \in \mathbb{Z}^+ : x \text{ is odd} \} \), which represents the set of all positive odd integers.
- Set \( B = \{-3, -1, 0, 2, 3, 5, 6, 9, 14 \} \).

The task is to find the intersection of sets \( A \) and \( B \), denoted by \( A \cap B \).

### Step-by-Step Solution:

1. **Identify Set \( A \)**: 
   Set \( A \) contains all positive odd integers. So, the elements of \( A \) could be: 
   \[
   A = \{ 1, 3, 5, 7, 9, 11, 13, 15, \dots \}
   \]

2. **Identify Set \( B \)**: 
   Set \( B \) is explicitly given as:
   \[
   B = \{-3, -1, 0, 2, 3, 5, 6, 9, 14\}
   \]

3. **Find \( A \cap B \)** (the intersection):
   - The intersection contains elements that are common to both \( A \) and \( B \).
   - From \( B \), the positive odd integers are \( 3, 5, 9 \).
   
   Therefore, \( A \cap B = \{ 3, 5, 9 \} \).

### Conclusion:
The correct set corresponding to \( A \cap B \) is \( \{3, 5, 9\} \), which matches option **A**.

Would you like more details on this solution or have any questions? 

Here are five related questions to deepen your understanding:
1. What is the intersection of two sets and how do you compute it?
2. Can the intersection of two disjoint sets be non-empty?
3. What is the union of sets \( A \) and \( B \)?
4. If \( A = \{ \text{positive even integers} \} \), what would \( A \cap B \) be?
5. What is the difference between an intersection and a union of two sets?

**Tip:** The intersection of two sets only includes elements that are in *both* sets. Always check for common elements!

Select the set corresponding to A ∩ B, where A = {x ∈ Z^+ : x is odd} and B = {-3, -1, 0, 2, 3, 5, 6, 9, 14}.

Learn how to find the intersection of sets A and B, where A contains positive odd integers and B contains a mix of integers. The correct set corresponding to A ∩ B is {3, 5, 9}. This problem explores key set theory concepts and is suitable for students in Grades 9-12.

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