Consensus theorem
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| Variable inputs | Function values | |||
| X | Y | Z | xy + x'z + yz | xy + x'z |
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 | 1 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 1 | 0 | 0 |
| 1 | 1 | 0 | 1 | 1 |
| 1 | 1 | 1 | 1 | 1 |
In boolean algebra, the consensus theorem is a simplification of the following terms:
- xy + x'z + yz = xy + x'z
The dual of this equation is:
- (x + y)(x' + z)(y + z) = (x + y)(x' + z)
