Symmetric difference of relationships

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Homework Help Overview

The discussion revolves around the symmetric difference of two relations, R1 and R2, defined on specific sets. Participants are examining the definition and calculation of the symmetric difference in the context of set theory.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are exploring different definitions of the symmetric difference, with one suggesting a definition involving union and intersection, while another proposes a definition based on set differences. There is a question regarding the correctness of the initial calculation of the symmetric difference.

Discussion Status

The discussion is active, with participants clarifying their definitions and confirming the correctness of the calculations. There is acknowledgment that the different definitions presented are equivalent, and one participant expresses a desire to further understand the concept through proof.

Contextual Notes

Participants are working within the constraints of homework rules, focusing on understanding the definitions and properties of the symmetric difference without providing complete solutions.

nicnicman
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Homework Statement


2. Let R1 = {(1,1),(1,2),(2,3),(3.4), (2,4) } and
R2 = {(1,1),(2,2),(2,3),(3,3),(3,4) } be relations from {1,2,3} to {1,2,3,4}

R1⨁ R2


Homework Equations





The Attempt at a Solution



R1⨁ R2 = {(1,2), (2,2), (2, 4), (3,3)}

Is this correct?
 
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If you defined

R_1\oplus R_2 = (R_1\cup R_2)\setminus (R_1 \cap R_2)

then your answer is correct.
 
Actually, I defined it as (R1 - R2) ∪ (R2 - R1). How's that?
 
nicnicman said:
Actually, I defined it as (R1 - R2) ∪ (R2 - R1). How's that?

That's the same thing as what I wrote. Maybe you want to prove it as an exercise. But in any case, your solution is fine!
 
Yeah, that would probably help me understand it better. Thanks.
 

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