Symmetric Difference Explanation

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Discussion Overview

The discussion revolves around demonstrating the equality of two set expressions, specifically (x\y) union (y\x) and (x union y) \ (y union x), using set theory laws. The scope includes mathematical reasoning and conceptual clarification related to set operations.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Conceptual clarification

Main Points Raised

  • One participant requests an explanation for the equality of two set expressions using set theory laws.
  • Another participant expresses suspicion that the question is a homework problem and refrains from providing extensive help.
  • Several participants suggest that the correct expression should involve (x union y) \ (x intersection y) instead of the original formulation.
  • A participant mentions that they are struggling to start the problem and seeks guidance on using absorption laws to rewrite the sets.
  • One participant advises applying set laws in various orders to find a solution, indicating a trial-and-error approach may be necessary.
  • Another participant provides a general strategy for understanding set operations by relating them to first-order logic and suggests using Venn diagrams for visualization.

Areas of Agreement / Disagreement

There is no consensus on the correct formulation of the set expressions, as participants suggest different interpretations and approaches. The discussion remains unresolved regarding the best method to demonstrate the equality.

Contextual Notes

Some participants express uncertainty about the absorption laws and how to apply them in this context. There are also references to the potential for misunderstanding the original problem statement.

gutnedawg
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Can someone explain to me how to show (x\y) union (y\x) = (x union y) \ (y union x) using only the main set theory laws for union, intersections and difference.
 
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I have a feeling that this is a homework problem, so I'm not going to tell you a lot.

How do you usually show the equality of sets?
 
hi gutnedawg! :wink:

shouldn't that be (x union y) \ (x intersection y) ?

anyway, start by writing x\y in terms of unions or intersections …

what do you get? :smile:​
 
tiny-tim said:
hi gutnedawg! :wink:

shouldn't that be (x union y) \ (x intersection y) ?

anyway, start by writing x\y in terms of unions or intersections …

what do you get? :smile:​
yea sorry I meant to write union and then intersection not union and union

this is not a homework problem this problem was posted in lecture for us to try on our own and I'm having trouble starting it

EDIT how could I write x\y in terms of intersections and unions... The professor suggested using the absorption laws but I'm not sure how to go on from rewriting x and y with the absorption laws
 
You've just got to apply the laws in different orders until you find the order that works. Trial and error, I'm afraid.
 
vertigo said:
You've just got to apply the laws in different orders until you find the order that works. Trial and error, I'm afraid.

care to give any hints?
 
hi gutnedawg! :smile:

(just got up :zzz: …)
gutnedawg said:
EDIT how could I write x\y in terms of intersections and unions... The professor suggested using the absorption laws but I'm not sure how to go on from rewriting x and y with the absorption laws

(what are the absorption laws? :confused:)

x\y = x intersection not-y :wink:​
 
General advice,
Set operations exactly mirror first order logic. Translate any set to the statement that some antecedent object is in the set. X --> "p is in X".

Then you can use your verbal skills to parse set operations...

x\y -> " p is in x and not in y".

A Venn diagram is also quite useful. Between Venn diagrams and translation to logic you can utilize your visual and verbal skills to better understand the set operations.

Finally ask yourself why your Professor didn't just tell you the answer and then trust his judgment. (Hint, you can't learn to swing a golf club by just watching the Pro's.)
 

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