Equivilence Relations And Classes Problems

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SUMMARY

The discussion centers on proving that the relation ~ is reflexive, symmetric, and transitive within the context of equivalence relations. User Pete seeks assistance with a specific problem, while user Steve provides a clear methodology for proving reflexivity by demonstrating that 0 = x - x is divisible by m for all integers x in Z. The symmetric and transitive properties can be proven using analogous reasoning. Pete confirms his understanding after receiving guidance.

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PeteSteve
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Hi guys

I am having trouble with this question (i have attached). Any help with it would be very much appreciated.

Many thanks in advance

Pete
 

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dear PeteSteve
you are expected to prove that the relation ~ is reflexiv,symmetric and transitive.
To show that ~ in 1a is reflexiv you must show that x ~ x for all x in Z . You can prove this by observing that 0 = x- x is divisible by m. The symmetric and transifive case can be proven in a similar way.
 
Hi dalle

I understand what I need to do now, thanks a lot for your help with the problem

Pete
 

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