Gesetze der boolschen Algebra
| ODER-Operation | ¦ | UND-Operation | |
| Kommutativgesetz: | A \(\vee\) B = B \(\vee\) A | ¦ | A \(\wedge\) B = B \(\wedge\) A |
| Assoziativgesetz: | A \(\vee\) (B \(\vee\) C) = (A \(\vee\) B) \(\vee\) C | ¦ | A \(\wedge\) (B \(\wedge\) C) = (A \(\wedge\) B) \(\wedge\) C |
| Distributivgesetz: | A \(\vee\) (B \(\wedge\) C) = (A \(\vee\) B) \(\wedge\) (A \(\vee\) C) | ¦ | A \(\wedge\) (B \(\vee\) C) = (A \(\wedge\) B) \(\vee\) (A \(\wedge\) C) |
| Absorbtionsgesetz: | A \(\vee\) (A \(\wedge\) B) = A | ¦ | A \(\wedge\) (A \(\vee\) B) = A |
| Komplementärgesetz: | A \(\vee\) \(\neg\)A = 1 | ¦ | A \(\wedge\) \(\neg\)A = 0 |
| Idempotenzgesetz: | A \(\vee\) A = A | ¦ | A \(\wedge\) A = A |
| Neutralitätsgesetz: | A \(\vee\) 0 = A | ¦ | A \(\wedge\) 1 = A |
| Extremalgesetz: | A \(\vee\) 1 = 1 | ¦ | A \(\wedge\) 0 = 0 |
| De Morgansches Gesetz: | \(\neg\)(A \(\vee\) B) = \(\neg\)A \(\wedge\) \(\neg\)B | ¦ | \(\neg\)(A \(\wedge\) B) = \(\neg\)A \(\vee\) \(\neg\)B |
| Involutionsgesetz: | \(\neg\)(\(\neg\)A) = A | ||
| Dualitätsgesetz: | \(\neg\)1 = 0 | \(\neg\)0 = 1 | |