1. Tożsamości, prawa de Morgana
Aksjomaty i tożsamości algebry Boole a
1. x+0=x
15. xy = x + y
2. xÅ"1=x
16. x + y = x Å" y
3. x+x=1
17. x+xy=x
4. xÅ"x=0
18. x(x + y)= x
5. x + y = y + x
19. xy + x y = x
6. x Å" y = y Å" x
20. (x+y)(x+y)=x
7. xy + xz = x(y + z)
21. x + yz =(x + y)Å"(x + z)
8. (x + y)(x + z)= x + yz
22. x + xy = x + y
9. x+1=1
10. x Å"0=0 23. x+y+z=x+(y+z)=(x+y)+z
11. x+x=x
24. x Å" y Å" z =(x Å" y)Å" z = x(y Å")
Å" z
12. xÅ"x=x
25. x(x + y)= xy
13. x=x
26. xy + yz + xz = xy + xz
14. x + xy = x + y
27. (x + y)(y + z)(x +)=(x + y)(x +)
z z
15, 16 Prawa de Morgana 17,18 reguły pochłaniania 19,20 reguły sklejania
Tożsamości do przerobienia:
(x + y)(x + z)= x + yz
x •" yx = x y
x(x + y)= x
x•"(x+y)=xy
x(x + y)= xy
x " y " xy = x + y
x + xy = x + y
x " y = x " y
xy + yz + xz = xy + xz
x•"y=x•"y
(x + y)(y + z)(x +)=(x + y)(x +)
z z
x •"(x + y)= xy
(x+y)(x+y)=x
x •" xy = x + y
x •" y •" xy = x + y
x + y + z = x(y + z)+ yz + xz