Binary operations AND and OR are distributive:
-
X
* (Y + Z) = X * Y + Y * Z à distribution of AND over OR.
-
(X
+ Y) + Z = X + (Y + Z) à distribution
|
x |
y |
z |
x+y |
x+z |
(x+y)(x+z) |
yz |
x+yz |
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
0 |
0 |
1 |
0 |
1 |
0 |
0 |
0 |
|
0 |
1 |
0 |
1 |
0 |
0 |
0 |
0 |
|
0 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
|
1 |
0 |
0 |
1 |
1 |
1 |
0 |
1 |
|
1 |
0 |
1 |
1 |
1 |
1 |
0 |
1 |
|
1 |
1 |
0 |
1 |
1 |
1 |
0 |
1 |
|
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |