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George BooleEnglish logician and mathematician
Publishes Investigation of theLaws of Thought in 1854
One-variable Theorems
OR Version AND Version
x | 0 = x
x | 1 = 1
x & 1 = x
x & 0 = 0
Note: Principle of Duality You can change | to & and 0 to 1 and vice versa
One-variable Theorems
OR Version AND Version
x | ~x = 1
x | x = x
x & ~x = 0
x & x = x
Note: Principle of Duality You can change | to & and 0 to 1 and vice versa
Associative Law
0 0 0 0 0 0 00 0 1 1 1 0 10 1 0 1 1 1 10 1 1 1 1 1 11 0 0 0 1 1 11 0 1 1 1 1 11 1 0 1 1 1 11 1 1 1 1 1 1
x y z y | z x | (y | z) x | y (x | y) | z
x | (y | z) = (x | y) | z