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| informatyka:podstawy-dzialania-komputera:prawa_algebry_boole_a [2024/04/10 11:41] – kawcix | informatyka:podstawy-dzialania-komputera:prawa_algebry_boole_a [2024/04/10 11:58] (current) – kawcix | ||
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| ====== 1.1 Prawa algebry Boole' | ====== 1.1 Prawa algebry Boole' | ||
| - | **Prawo przemienności** | + | ===== Prawo przemienności |
| + | |||
| **A + B = B + A** czyli **A or B = B or A** | **A + B = B + A** czyli **A or B = B or A** | ||
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| - | **Prawo łączności** | + | ===== Prawo łączności |
| **(A + B) + C = A + (B + C)** czyli **(A or B ) or C = A or ( B or C )** | **(A + B) + C = A + (B + C)** czyli **(A or B ) or C = A or ( B or C )** | ||
| Line 20: | Line 23: | ||
| ---- | ---- | ||
| - | **Prawo rozdzielności** | + | ===== Prawo rozdzielności |
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| ---- | ---- | ||
| - | **Twierdzenie 4** | + | ===== Twierdzenie 4 ===== |
| **A + A = A** czyli **A or A = A** | **A + A = A** czyli **A or A = A** | ||
| Line 41: | Line 46: | ||
| ---- | ---- | ||
| - | **Twierdzenie 5** | + | ===== Twierdzenie 5 ===== |
| znak ¬ to negacja. | znak ¬ to negacja. | ||
| - | **AB + A¬B = A** czyli **(A and B) or (A and not(B)) | + | **AB + A¬B = A** czyli **(A and B) or (A and not(B))** |
| - | ** | + | |
| **(A + B) (A + ¬B) = A** czyli **(A or B) and (A or not(B)) = A** | **(A + B) (A + ¬B) = A** czyli **(A or B) and (A or not(B)) = A** | ||
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| ---- | ---- | ||
| - | **Prawo Absorbcji** | + | ===== Prawo Absorbcji |
| **A + AB = A** czyli **A or (A and B) = A** | **A + AB = A** czyli **A or (A and B) = A** | ||
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| ---- | ---- | ||
| - | Twierdzenie 7 | + | ===== Twierdzenie 7 ===== |
| **0 + A = A** czyli **0 or A = A** | **0 + A = A** czyli **0 or A = A** | ||
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| ---- | ---- | ||
| - | Twierdzenie 8 | + | ===== Twierdzenie 8 ===== |
| **1 + A = A** czyli **1 or A = A** | **1 + A = A** czyli **1 or A = A** | ||
| - | **1A = A** czyli **1 AND A = a** | + | **1A = A** czyli **1 and A = A** |
| ---- | ---- | ||
| - | **Prawo pochłaniania** | + | ===== Prawo pochłaniania |
| - | **¬A + A = 1** czyli **not(a) or a = 1** | + | |
| + | **¬A + A = 1** czyli **not(A) or A = 1** | ||
| **¬AA = 0** czyli **(not(A) and A) = 0** | **¬AA = 0** czyli **(not(A) and A) = 0** | ||
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| ---- | ---- | ||
| - | **Twierdzenie 10** | + | ===== Twierdzenie 10 ===== |
| - | A + ¬AB = A + B czyli A or (not(a) AND B) = A or B | ||
| - | A(¬A + B ) = AB czyli A and (not(A) or B) = A and B | + | **A + ¬AB = A + B** czyli **A or (not(A) and B) = A or B** |
| + | |||
| + | **A(¬A + B ) = AB** czyli **A and (not(A) or B) = A and B** | ||
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| - | **Prawa de Morgana** | + | ===== Prawa de Morgana |
| - | ¬(a + b) = ¬a¬b czyli not(A or B) = not(A) and not(B) | + | **¬(a + b) = ¬a¬b** czyli **not(A or B) = not(A) and not(B)** |
| - | ¬(AB) = ¬A or ¬B czyli not(A and B) = not(A) or not(B) | + | **¬(AB) = ¬A or ¬B** czyli **not(A and B) = not(A) or not(B)** |