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Simplification Rules
[^] Boolean Expression Simplification   [^^][^^] Binary/Boolean Main Index
[Truth Table Examples] [Boolean Expression Simplification] [Logic Gate Examples]
Here is the list of rules used for the boolean expression simplifications. This is a fairly standard list you could find most anywhere, but we thought you needed an extra copy.
The Idempotent Laws
AA = A
A+A = A
The Associative Laws
(AB)C = A(BC)
(A+B)+C = A+(B+C)
The Commutative Laws
A+B = B+A
The Distributive Laws
A(B+C) = AB+AC
A+BC = (A+B)(A+C)
The Identity Laws
AF = F
AT = A
A+F = A
A+T = T
The Complement Laws
AA = F
A+A = T
F = T
T = F
The Involution Law
A = A
DeMorgan's Law
AB = A+B
A+B = A B

Browser note: The Involution law is “not not A equals A;” there should be two lines above the first A. It renders reasonably in Firefox and IE 7, and hopefully in whatever you're using. I found four different ways that work in Firefox, but only the most complicated one also works in IE. (I haven't tried in IE 6 and don't want to fool with it.)