now knowing this reanswer this using the question: *A*={*x*∈Z:*x* is odd}

B={2,4,6,7,11,12}*B*={2,4,6,7,11,12}

C={1,3,4,6,8,11,13}*C*={1,3,4,6,8,11,13}

Let's analyze the sets given:

1. **Set \( A \)** is defined as:
   \[
   A = \{ x \in \mathbb{Z} \mid x \text{ is odd} \}
   \]
   This means \( A \) contains all odd integers.

2. **Set \( B \)** is:
   \[
   B = \{ 2, 4, 6, 7, 11, 12 \}
   \]
   Set \( B \) contains specific integers, both even and odd.

3. **Set \( C \)** is:
   \[
   C = \{ 1, 3, 4, 6, 8, 11, 13 \}
   \]
   Set \( C \) also contains specific integers, both even and odd.

### 1. Elements in \( A \cap B \) (Intersection of \( A \) and \( B \)):
   The intersection consists of elements that are both in \( A \) and \( B \). Since \( A \) contains all odd integers and \( B \) contains \( 2, 4, 6, 7, 11, 12 \), the odd integers common to both are:
   \[
   A \cap B = \{ 7, 11 \}
   \]

### 2. Elements in \( A \cap C \) (Intersection of \( A \) and \( C \)):
   The intersection consists of elements that are both in \( A \) and \( C \). Since \( A \) contains all odd integers and \( C \) contains \( 1, 3, 4, 6, 8, 11, 13 \), the odd integers common to both are:
   \[
   A \cap C = \{ 1, 3, 11, 13 \}
   \]

### 3. Elements in \( B \cup C \) (Union of \( B \) and \( C \)):
   The union consists of all elements from both \( B \) and \( C \), without repetition:
   \[
   B \cup C = \{ 1, 2, 3, 4, 6, 7, 8, 11, 12, 13 \}
   \]

### 4. Elements in \( B \setminus C \) (Difference of \( B \) and \( C \)):
   The difference \( B \setminus C \) consists of elements that are in \( B \) but not in \( C \):
   \[
   B \setminus C = \{ 2, 7, 12 \}
   \]

### 5. Elements in \( C \setminus B \) (Difference of \( C \) and \( B \)):
   The difference \( C \setminus B \) consists of elements that are in \( C \) but not in \( B \):
   \[
   C \setminus B = \{ 1, 3, 8, 13 \}
   \]

Let me know if you want details on any of these calculations or have other questions.

Here are 5 related questions:
1. What is \( A \cup B \) (Union of \( A \) and \( B \))?
2. What is \( A \cap (B \cup C) \) (Intersection of \( A \) and the union of \( B \) and \( C \))?
3. What is \( A \setminus B \) (Difference of \( A \) and \( B \))?
4. What is the symmetric difference \( B \Delta C \) (Elements in either \( B \) or \( C \) but not in both)?
5. How many elements are in \( A \cap (B \cap C) \) (Intersection of \( A \) with the intersection of \( B \) and \( C \))?

**Tip:** When dealing with set operations, it's helpful to visualize the sets using a Venn diagram to understand the relationships between different sets more clearly.

A = {x ∈ Z : x is odd}, B = {2, 4, 6, 7, 11, 12}, C = {1, 3, 4, 6, 8, 11, 13}

Explore the set operations for A = {x ∈ Z : x is odd}, B = {2, 4, 6, 7, 11, 12}, and C = {1, 3, 4, 6, 8, 11, 13}. Learn how to find the intersection, union, and difference between these sets. Suitable for students in Grades 9-12.

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