Verifying Identity: Easier Way to Solve?

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Discussion Overview

The discussion revolves around verifying a mathematical identity involving set operations, specifically the symmetric difference and set complements. Participants explore methods for simplifying the verification process, including the use of Venn diagrams.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant seeks a simpler method to verify the identity involving set operations.
  • Another participant suggests using a Venn diagram as a potential solution.
  • A third participant confirms that they used Venn diagrams to arrive at the desired result, mentioning the involvement of seven disjoint sets.

Areas of Agreement / Disagreement

Participants appear to agree on the utility of Venn diagrams for this problem, but there is no explicit consensus on the simplicity of the methods or the correctness of the identity verification.

Contextual Notes

The discussion does not resolve potential issues with negations or the complexity of the verification process, and it does not clarify the definitions or properties of the symmetric difference being used.

Who May Find This Useful

Individuals interested in set theory, mathematical identities, or those looking for alternative methods to verify mathematical expressions may find this discussion relevant.

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I need to verify this identity:

(A\B)[itex]\Delta[/itex]C = (A[itex]\Delta[/itex]C)[itex]\Delta[/itex](A[itex]\bigcap[/itex]B)

(with delta standing for the symmetric difference, I don't know the proper latex code) I've tried it "brute force" several times, working out each side and simplifying it until the sides are equal (it's likely that I'm messing up a negation somewhere) and I've found this method rather cumbersome. Is there any simpler way to solve this?
 
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Hi autre! :smile:

Have you tried drawing a so called Venn diagram?
 
I used Venn diagrams and got the result you are looking for. There are 7 disjoint sets involved. Is that the brute force you tried?
 
That's it, mathman. Thanks guys.
 

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