If `S=R,A={x:-3lexlt7} and B={x:0ltxlt10}`, the number of positive integers in `ADeltaB` is

Explanation

To solve the problem, we need to find the number of positive integers in the symmetric difference of sets A and B, denoted as \( A \Delta B \). The symmetric difference is defined as \( A \Delta B = (A - B) \cup (B - A) \).

### Step-by-Step Solution:

1. **Define the Sets A and B**:
- Set \( A = \{ x : -3 \leq x < 7 \} \)
- Set \( B = \{ x : 0 < x < 10 \} \)

2. **List the Elements of Set A**:
- The integers in set A from -3 to 7 (excluding 7) are:
\[ A = \{-3, -2, -1, 0, 1, 2, 3, 4, 5, 6\} \]

3. **List the Elements of Set B**:
- The integers in set B from 0 to 10 (excluding 0 and 10) are:
\[ B = \{1, 2, 3, 4, 5, 6, 7, 8, 9\} \]

4. **Calculate \( A - B \)**:
- We need to find the elements in A that are not in B:
- \( A - B = A \setminus B = \{-3, -2, -1, 0\} \)

5. **Calculate \( B - A \)**:
- We need to find the elements in B that are not in A:
- The elements in B that are not in A are \( \{7, 8, 9\} \) since 1, 2, 3, 4, 5, and 6 are common in both sets.
- Thus, \( B - A = \{7, 8, 9\} \)

6. **Find \( A \Delta B \)**:
- Now, we combine the results from steps 4 and 5:
\[ A \Delta B = (A - B) \cup (B - A) = \{-3, -2, -1, 0\} \cup \{7, 8, 9\} \]
- Therefore,
\[ A \Delta B = \{-3, -2, -1, 0, 7, 8, 9\} \]

7. **Count the Positive Integers in \( A \Delta B \)**:
- The positive integers in \( A \Delta B \) are \( \{7, 8, 9\} \).
- The count of positive integers is 3.

### Final Answer:
The number of positive integers in \( A \Delta B \) is **3**.