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An Introduction to STEM Programming with Python — 2019-09-03a Page 244
Bonus Chapter 4 — Simplification of Boolean Expressions

Free
Example Simplification — Three

F(X,Y,Z) = XY + X’Z + Y(X+Z) + (Z(X+Y)(Z+Y))’ Distributive
XY + X’Z + YX + YZ + (Z(X+Y)(Z+Y))’
XY + X’Z + YZ + (Z(X+Y)(Z+Y))’ Idempotency
XY + X’Z + (Z(X+Y)(Z+Y))’ Consensus
eBook DeMorgan’s
XY + X’Z + Z’ + (X+Y)’ + (Z+Y)’
DeMorgan’s
XY + X’Z + Z’ + X’Y’ + Z’Y’
XY + X’Z + Z’ + X’Y’
Absorption
XY + X’ + Z’ + X’Y’
Absorption
XY + X’ + Z’ Simplification
Y + X’ + Z’ Simplification
Edition

Summary

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Important Terms

• Absorption • DeMorgan's Law • Null Law
• Associative Law • Distributing Nots • Postulates
•
Simplification
• Closure • Distributive Law Free
• Commutative Law • Idempotency • Theorems
• Compliment Law • Identity
• Consensus • Involution

Exercises

1. Show proof for Theorem 1(a): Null Law eBook
X + 1 = 1

2. Show proof for Theorem 2: Involution
X'' = X

3. Show proof for Theorem 3: Idempotency Edition
a) X + X = X

Copyright 2019 — James M. Reneau Ph.D. — http://www.syw2l.org — This work is licensed
under a Creative Commons Attribution-ShareAlike 4.0 International License.