informatyka:podstawy-dzialania-komputera:prawa_algebry_boole_a [Kawcix Wiki]

This page is read only. You can view the source, but not change it. Ask your administrator if you think this is wrong.

====== 1.1 Prawa algebry Boole'a  ======

===== Prawo przemienności =====
 


**A + B = B + A** czyli **A or B = B or A**

**AB = BA** czyli **A and B = B and A** 


----


===== Prawo łączności =====


**(A + B) + C = A + (B + C)** czyli **(A or B ) or C = A or ( B or C )**

**(AB)C = A(BC)** czyli **(A and B) and C = A and (B and C)**


----

===== Prawo rozdzielności =====



**A(B + C)** = **AB + AC**  czyli **A and ( B or C)** = **(A and B) or (A and C)** 


**A + (BC) = (A + B)(A + C)** czyli** A or ( B and C) = (A or B) and (A or C)
**


----

===== Twierdzenie 4 =====


**A + A = A** czyli  **A or A = A**

**AA = A** czyli **A and A = A**


----

===== Twierdzenie 5 =====


znak ¬ to negacja.

**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**



----

===== Prawo Absorbcji =====


**A + AB = A** czyli **A or (A and B) = A**

**A(A+B) = A** czyli **A and (A or B) = A**


----

===== Twierdzenie 7 =====


**0 + A = A** czyli **0 or A = A**

**0A = 0** czyli **0 and A = A** 


----

===== Twierdzenie 8 =====


**1 + A = A** czyli **1 or A = A**

**1A = A** czyli **1 and A = A** 


----

===== Prawo pochłaniania =====


**¬A + A  = 1** czyli **not(A) or A = 1**

**¬AA = 0** czyli **(not(A) and A) = 0** 


----

===== 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**


----


===== Prawa de Morgana =====


**¬(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)**