The identity law comes as a pair:
- = A
- = A
0 is the "do nothing" value for OR, and 1 is the "do nothing" value for AND. That mirrors ordinary arithmetic, where adding 0 or multiplying by 1 changes nothing.
You can confirm it by trying both values of A. For : 0 + 0 = 0 and 1 + 0 = 1, so the result always equals A.
In a circuit, it says an OR gate with one input tied to 0 just passes the other input through, and so does an AND gate with one input tied to 1.
It is the law you use most often to clean up after other steps. After the complement law turns into 1, the identity law turns back into A. The two forms are each other's dual.
| 0 | 0 | 0 |
| 1 | 1 | 1 |