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

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Discussion Overview

The discussion revolves around a specific step in Boolean algebra simplification, particularly focusing on the expression (NOT A)(NOT B)(C) + B and its equivalence to (NOT A)(C) + B. Participants are exploring the reasoning behind the disappearance of the NOT B term.

Discussion Character

  • Homework-related

Main Points Raised

  • One participant expresses confusion about the simplification step, questioning what happens to the NOT B term in the expression.
  • Another participant suggests expanding the right-hand side of the equation to aid in understanding the simplification process.
  • A different participant proposes an alternative approach by expanding B in a specific way to illustrate how the left-hand side can be manipulated to yield a simplified form.
  • There is a follow-up acknowledgment from the original poster indicating some understanding after the suggestions.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the best approach to understand the simplification, as different methods are proposed without agreement on a single correct path.

Contextual Notes

Some steps in the simplification process are not fully resolved, and there are assumptions made about the manipulation of Boolean expressions that may not be universally applicable.

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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