How to Further Simplify the Expression (A + A*B)?

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SUMMARY

The discussion focuses on simplifying the Boolean expression (xy’+z)’.((xz)’+y’). The solution provided demonstrates the application of Boolean algebra rules, resulting in the expression being simplified to x’ + x’z’ + x’y’ + yz’ + z’. The participants confirm that further simplification is possible, specifically addressing the expression A + A*B, which can be simplified to A using the Absorption Law.

PREREQUISITES
  • Understanding of Boolean algebra principles
  • Familiarity with the Absorption Law in Boolean expressions
  • Knowledge of De Morgan's Theorems
  • Experience with simplifying logical expressions
NEXT STEPS
  • Study Boolean algebra simplification techniques
  • Learn about De Morgan's Theorems in detail
  • Explore the Absorption Law and its applications
  • Practice simplifying complex Boolean expressions using truth tables
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Students studying digital logic design, computer engineers, and anyone interested in optimizing Boolean expressions for circuit design.

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Homework Statement


(xy’+z)’.((xz)’+y')


The Attempt at a Solution


(xy’+z)’.((xz)’+y’)
=(x'+yz’).(x’+z’+y’)
=x’x’ + x’z’ + x’y’ + yz’x’ + yz’z’ + yz’y’
=x’ + x’z’ + x’y’ + yz’x’ + yz’ + z’

Can it be further siplify?
 
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Yes it can.

How can you simplify A + A*B?
 

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