Sets A and B have `3` and `6` elements each. The maximum possible number of elements in A-B is __________

Answer

To solve the problem of finding the maximum possible number of elements in the set difference \( A - B \) where set \( A \) has 3 elements and set \( B \) has 6 elements, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Sets**:
- Let set \( A \) have 3 elements. For example, we can represent it as \( A = \{a_1, a_2, a_3\} \).
- Let set \( B \) have 6 elements. We can represent it as \( B = \{b_1, b_2, b_3, b_4, b_5, b_6\} \).

2. **Define Set Difference**:
- The set difference \( A - B \) consists of elements that are in set \( A \) but not in set \( B \).
- Mathematically, \( A - B = \{ x \in A | x \notin B \} \).

3. **Maximize \( A - B \)**:
- To maximize the number of elements in \( A - B \), we need to ensure that none of the elements of set \( A \) are present in set \( B \).
- This means we can choose elements for set \( A \) that are completely distinct from those in set \( B \).

4. **Count the Elements**:
- If we select elements for set \( A \) such that none of them are in set \( B \), then all 3 elements of set \( A \) will be included in \( A - B \).
- Therefore, the maximum possible number of elements in \( A - B \) is equal to the number of elements in \( A \), which is 3.

5. **Conclusion**:
- Thus, the maximum possible number of elements in \( A - B \) is \( 3 \).

### Final Answer:
The maximum possible number of elements in \( A - B \) is **3**.