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Laws of Boolean Algebra

The laws of Boolean algebra can be defined :

    • axiomatically: as certain equations called axioms together with their logical consequences called theorems
    • semantically: as those equations that are true for every possible assignment of 0 or 1 to their variables.

In computing we usually come across Boolean algebra when we consider collections of logic gates. (See the electronics section of Cyberphysics for more information on this).

complimentarity . = + =
laws of 1s and 0s . = + =
identities . = + =
indempotent law . = + =
commutativity . = . + = +
associativity (.) = (.) ( + ) + = + ( + )
distribution ( + ) = . + . + . = ( + ).( + )
uniting theorem #1 . + = ( + ). =
uniting theorem #2 . + = + ( + ). = .
De Morgan's Law = + = .