Álgebra Booleana
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Formulas:
Axiomas del algebra Booleana
| 1a | 0 x 0 = 0 | |
| 1b | 1 + 1 = 1 | |
| 2a | 1 x 1 = 1 | |
| 2b | 0 + 0 = 0 | |
| 3a | 0 x 1 = 1 x 0 = 0 | |
| 3b | 1 + 0 = 0 + 1 = 1 | |
| 4a | Si x = 0, entonces x = 1 | |
| 4b | Si x = 1, entonces x = 0 | |
Teoremas de una sola variable
| 5a | x · 0 = 0 | |
| 5b | x + 1 = 1 | |
| 6a | x · 1 = 1 | |
| 6b | x + 0 = x | |
| 7a | x · x = x | |
| 7b | x + x = x | |
| 8a | x · x̄ = 0 | |
| 8b | x + x̄ = 1 | |
| 9 | x̄ = x | |
Propiedades de dos y tres variables
| 10a | x · y = y · x | Conmutativa |
| 10b | x + y = y + x | |
| 11a | x · (y · z) = (x · y) + z | Asociativa |
| 11b | x + (y + z) = (x + y) + z | |
| 12a | x · (y + z) = x · y + x · z | Distributiva |
| 12b | x + y · z = (x + y) · (x + z) | |
| 13a | x + x · y = x | Absorci처n |
| 13b | x · (x + y) = x | |
| 14a | x · y + x · ỹ = x | Combinaci처n |
| 14b | (x + y) · (x + ỹ) = x |
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