Table 1 Part of Boolean algebra functions
From: Automatic evaluation technique for certain types of open questions in semantic learning systems
Description | OR form | AND form |
|---|---|---|
Axiom 1 | x + 0 = x | x · 1 = x |
Axiom 2 | x + y = y +x | x · y = y · x |
Axiom 3 | x ·(y + z) = (x · y) + (x · z) | x + y · z = (x + y) · (x + z) |
Axiom 4 | x + x’ = 1 | x · x’ = 0 |
Theorem 1 | x + x = x | x · x = x |
Theorem 2 | x + 1 = 1 | x · 0 = 0 |
Theorem 3 | (x’) = x |  |
Associativity | x + (y + z) = (x + y) + z | x · (y · z) = (x · y) · z |
Absorption | x + x · y = x | x · (x + y) = x |
DeMorgan’s Law | (x + y)’ = x’ · y’ | (x · y)’ = x’ + y’ |