Combining is the main way variables disappear in simplification:
- = X
- Dual: = X
It is not a new law. It is three laws in a row: = (distributive) = (complement) = X (identity).
Intuition. If the output is 1 whether Y is 0 or 1, then Y does not matter, so you can leave it out.
The condition is strict: the two terms must differ in exactly one variable, and in that variable only by its bar. differs in both B and C, so it does not combine.
Two terms that can combine like this are called adjacent. For minterms, adjacent means their binary codes differ in exactly one bit; see adjacent minterms. Combining in rounds, then removing redundant terms, is the whole idea behind Karnaugh maps, where adjacent cells sit next to each other.
A term can combine with more than one partner: copy it first with the idempotent law.
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 | 0 |
| 1 | 0 | 0 | 1 | 1 |
| 1 | 0 | 1 | 1 | 1 |
| 1 | 1 | 0 | 0 | 0 |
| 1 | 1 | 1 | 0 | 0 |