Here are a couple of examples using addition and multiplication, assuming you can reuse numbers:
Example 1 (using only 2 and 3):
* 1: 3 - 2
* 2: 2
* 3: 3
* 4: 2 + 2
* 5: 3 + 2
* 6: 2 * 3
* 7: 3 + 2 + 2
* 8: 2 * 2 * 2
Example 2 (using only 1 and 2):
This example requires more complex operations. It's difficult to generate all numbers from 1 to 8 using *only* 1 and 2 with just two operations unless you allow exponentiation. For simplicity, let's demonstrate with a limited set:
* 1: 1
* 2: 2
* 3: 2 + 1
* 4: 2 * 2
* 8: 2 * 2 * 2
To create a complete solution for 1-8 using only two operations and a limited set of numbers, you'd need to specify the allowable operations and numbers. There might not even be a solution if you restrict the options too much.