derived Boolean operations
From these operations, define the following “derived” operations (on ): for
Notice that the operators and are dual of and respectively.
It is evident that these derived operations (and indeed the entire theory of Boolean algebras) owe their existence to those operations and connectives that are found in logic and set theory, as the following table illustrates:
|or or||complement||logical not||complement|
|bottom element||falsity||empty set|
|or||symmetric difference||symmetric difference (http://planetmath.org/SymmetricDifference)|
|Sheffer stroke||Sheffer stroke|