Definition of Boolean Algebra
A non empty set B, together with two binary operations `+` and `*` defined on it, is said to be boolean algebra,
if the following laws hold:
(1) Commutative laws
`AA x,y in B`, `x+y=y+x` and `x*y=y*x`
(2) Associative laws
`AA x,y,z in B`, `(x+y)+z=x+(y+z)` and `(x*y)*z=x*(y*z)`
(3) Distributive laws
`AA x,y,z in B`, `x*(y+z)=x*y+x*z` and `x+(y*z)=(x+y)*(x+z)`
(4) Existence of identity elements
`EE 0,1 in B` such that `x+0=x` and `x*1=x`
(5) Existence of complement
for each `x in B`, `EE x' in B` such that `x+x'=1` and `x*x'=0`
This material is intended as a summary. Use your textbook for detail explanation.
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