Proving the Distributive Property of XOR in Boolean Algebra

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Homework Help Overview

The discussion revolves around proving the distributive property of XOR in Boolean algebra, specifically the expression x(y ⊕ z) = xy ⊕ xz. Participants are exploring the definitions and properties of XOR and its relation to other Boolean operations.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are considering the use of truth tables and expanding expressions to demonstrate equivalence. There are questions about what has been attempted so far and suggestions to use de Morgan's laws.

Discussion Status

The discussion is ongoing, with some participants expressing frustration over a lack of progress. There is a suggestion that sharing previous attempts could lead to identifying missing steps. Guidance has been offered regarding expansion and the application of de Morgan's laws.

Contextual Notes

Some participants indicate that they have not made significant progress on the problem, which may affect the depth of the discussion. There is an acknowledgment of homework constraints and the pressure of deadlines.

Tony11235
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With [tex]x \oplus y[/tex] defined to be (here I'm using x' as the complement of x) xy'+x'y, prove [tex]x(y \oplus z) = xy \oplus xz[/tex]

I'm stuck. Any hint or help would be great.
 
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Well, what have you done so far?

(I presume xy is the "and" operation, and x+y is the "or" operation?)
 
Would a truth table work?
 
You can just expand out both expressions and see they are the same. You will need to use de Morgan's laws to turn the complement of a product into a sum of complements, however. That is the only tricky part.
 
Have you done anything on this problem, or just sit and stared at it?
 
Hurkyl said:
Have you done anything on this problem, or just sit and stared at it?

I expanded the right side, thought deeply about it, tried a few other moves, but came up short and had to turn it in unfinished. Oh well, one low homework score won't kill me.
 
Well, if you had showed what you had done, maybe we could have pointed out the key step you were missing. Oh well. :frown:
 

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