This document discusses Boolean algebra which includes the laws of identity, noncontradiction, excluded middle, and rational inference. It also discusses how relationships in Boolean algebra are limited to true or false values. The document provides an example of simplifying a Boolean logic circuit using the distributive law to factor out common terms, reducing the number of logic gates from five to two and simplifying the overall circuit.
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3. The Law of Identity
(A is A)
The Law of Noncontradiction
(A is not equal to A)
The Law of Excluded Middle
(Either A or A)
The Law of Rational Inference
(Process of Elimination)
9. AB + BC ( B + C )
AB + BBC + BCC
AB + BC + BC
AB + BC
B ( A + C )
DISTRIBUTING
TERMS
APPLYING IDENTITY ( AA = A )
APPLYING IDENTITY ( A + A = A )
FACTOR B OUT OF TERMS
10. A
C
B
B ( A + C )
A + C
This circuit is much simpler than
the original,
Having two logic gates instead of
five.