From: "David S. Alexander" <d.s.alexander@gte.net>
Subject: Boolean Law Title needed
Date: Thu, 05 Oct 2000 07:42:21 GMT
Newsgroups: sci.math
Summary: Axioms for Boolean algebras

I am hoping that someone will have the answer to a question. I am a student
in a class on digital logic design. We use Boolean algebra to simplify
functions before designing the corresponding circuits. Reducing the number
of terms makes for a simpler circuit which is less expensive to build.

Our teacher has provided us with 10 laws. (Please excuse my use of primes
instead of overbars to signify NOT. I hope that "·" is legible and the AND
multiplication dot operator on UNIX and Macintosh computers.):

involution: (x')' = x
identity: x + 0 = x and x·1 = x
dominance: x + 1 = 1 and x·0 = 0
idempotent: x + x = x and x·x = x
complement: x + x' = 1 and x·x' = 0
commutative: x + y = y + x and x·y = y·x
associative: x + (y + z) = (x + y) + z and (x·y)·z = x·(y·z)
distributive: x·(y + z) = xy + xz and x + yz = (x + y)·(x + z)
absorption: x + xy = x and x·(x + y) = x

The tenth law, however, he does not have a name for. He simply refers to it
as "Ms. Pacman". I doubt that earlier logical mathematicians played video
games much.

The law is: A + (A'·B) = A + B

I know that it can be derived from combining the Distributive and Identity
Laws, but am wondering if anyone knows of a name for it. I found a few
digital logic instructors that lumped it together with the absorption law
and a few others as "Simplification Laws", but I am really wondering if it
has a distinct, standard name.

Any help that anyone could provide would be appreciated.

Best regards,

David Alexander