Okay, So I just got done reading and re-reading Chapter one of Introductory Real Analysis by Andrei Kolmogorov and S.V Fomin, I have to say it is a lot easier to read than the symbolic logic book I have. But to the point, There is this section which talks about Boolean Rings and it defines them just as you would define any Boolean Algebra by the intersection of any sets must be in the Algebra(Ring) and the symmetric difference between any two sets must be in the Algebra(Ring).(adsbygoogle = window.adsbygoogle || []).push({});

My problem begins not with the definition, but with the concept of the Boolean Lattice ##BL_n## and n is at least 1. So when you create this Boolean Lattice and it's similar to a Boolean Algebra's/(Ring's) Power Set, right? Also, If it is the power set of The Boolean Algebra(Ring), then would it mean that the ##BL_n## is a semi ring of the Boolean Algebra(Ring), or what? I mean the definition of a semi ring is that, if you take any two subsets of The ring, lets call it ##\mathcal{X}## and take their intersection then, this intersection must be in ##\mathcal{X}##. Furthermore, that ##\mathcal{X}## contains the empty set and all sets can be represented as a finite, or countably infinite cover of that set. Next natural question, is the semi ring ##\mathcal{X}## a powerset?

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# Boolean Rings: System of Switches.

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