Boolean Algebra Simplification Property Question

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Discussion Overview

The discussion revolves around the simplification of a Boolean algebra expression, specifically the transformation of the expression r*c'w + c to c + wr. Participants explore the properties of Boolean algebra that apply to this simplification, including the potential use of the Absorption principle and the Distributive property.

Discussion Character

  • Technical explanation, Debate/contested, Homework-related

Main Points Raised

  • One participant suggests that the simplification uses the Absorption principle.
  • Another participant counters that the simplification follows from the Distributive property of OR over AND, along with the Complementation principle x OR x' = 1.
  • A later reply clarifies that the problem is a worked example intended for extra practice, reinforcing the use of the Distributive property and complement theory.
  • One participant questions whether functionally equivalent expressions can always be reduced to being identical, assuming that they can since they are equal.
  • Another participant states that two Boolean expressions are equal if and only if they have identical truth tables.

Areas of Agreement / Disagreement

Participants express differing views on which Boolean simplification properties apply to the expression. There is no consensus on the specific property used, and the discussion remains unresolved regarding the conditions under which equivalent expressions can be reduced to identical forms.

Contextual Notes

Participants discuss the implications of functional equivalence in Boolean expressions, but the limitations of their claims regarding simplification properties and truth table equivalence are not fully explored.

Bigworldjust
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Hi I am not sure where to post this question but I am trying to simplify this expression:

r*c'w+c (As in R AND NOT C AND W OR C) to c+wr (As in C OR W AND R) and I know that it simplifies to this and they are both equivalent; however my question is which boolean simplification property is used here? Is it the Absorption principle? Thank you!
 
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No, I don't think so. It follows from the distributive property of OR over AND, combined with the compementation principle x OR x' = 1.

Is this homework?
 
MisterX said:
No, I don't think so. It follows from the distributive property of OR over AND, combined with the compementation principle x OR x' = 1.

Is this homework?

No it's a worked example left for us to solve if we wanted extra practice. And that's what I thought initially. So it is using the distributive property and then the complement theory. Thank you.
 
Also one last question. When expressions are functionally equivalent like the two above, can they always be reduced to being identical? I am assuming yes, because they are equal to begin with, correct?
 
Two Boolean expressions that have the same variables are equal if and only if they have identical truth tables.
 

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