Why (NOT A)(NOT B)(C) + B = (NOT A)(C) + B [Boolean Algebra]

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SUMMARY

The discussion centers on simplifying Boolean algebra expressions, specifically the equation (NOT A)(NOT B)(C) + B = (NOT A)(C) + B. The key step involves recognizing that the term (NOT B) can be effectively eliminated through strategic expansion and simplification. By expanding B as (¬A)(C)(B) + B, the left-hand side can be transformed and simplified to yield (¬A)(C), confirming the equality. This demonstrates the importance of understanding Boolean simplification techniques in function simplification.

PREREQUISITES
  • Understanding of Boolean algebra principles
  • Familiarity with function simplification techniques
  • Knowledge of logical operators (AND, OR, NOT)
  • Experience with algebraic manipulation of expressions
NEXT STEPS
  • Study Boolean algebra simplification techniques in-depth
  • Learn about Karnaugh maps for visual simplification
  • Explore the application of De Morgan's Theorems in simplification
  • Practice with various Boolean expressions and their simplifications
USEFUL FOR

Students studying Boolean algebra, educators teaching logic design, and anyone involved in digital circuit design or computer science fundamentals.

rehcarlos
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Homework Statement


I'm studying function simplification in boolean algebra, and I didnt understand the following step:
(NOT A)(NOT B)(C) + B = (NOT A)(C) + B

What happened to the NOT B?

Homework Equations


The Attempt at a Solution

 
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Expand (¬A)(C) on the right hand side as (¬A)(¬B)(C)+(¬A)(B)(C) and simplify.
 
Hey DH thanks for helping,

but I still don't get it, I mean...

I need to know what's the next step of (NOT A)(NOT B)(C) + B. In your answer, you are saying that I need to expand the right side... but in a real exercise, I wouldn't know what the right side would look like
 
On the left hand side, then.

Expand B as B = (any boolean expression whatsoever)B + B. Here we'll use B = (¬A)(C)(B) + B. Then the left hand side becomes (¬A)(¬B)(C) + (¬A)(C)(B) + B. Combine the first two terms and simplify to yield (¬A)(C).
 
Got it! Thanks
 
test
 

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