State true or false in each of the following statements.
The identity element for division for integers is 1.

Answer

To determine whether the statement "The identity element for division for integers is 1" is true or false, let's analyze the concept of identity elements in division.

### Step-by-Step Solution:

1. **Understanding Identity Element**:
- An identity element for a particular operation is a value that, when used in that operation with any number, returns the original number.
- For example, in addition, the identity element is 0 because any number plus 0 is the number itself (e.g., 5 + 0 = 5).

2. **Applying to Division**:
- For division, we need to check if dividing any integer by 1 returns the original integer.
- If we take an integer \( a \), dividing it by 1 gives us \( a \div 1 = a \). This part holds true.

3. **Checking the Reverse**:
- Now, let's check if dividing 1 by any integer \( a \) gives us back \( a \).
- For instance, if we take \( a = 5 \), then \( 1 \div 5 = 0.2 \), which is not equal to 5.

4. **Conclusion**:
- Since dividing 1 by any integer does not return the integer itself, we conclude that the identity element for division is not 1.
- Therefore, the statement "The identity element for division for integers is 1" is **False**.

### Final Answer:
**False**