Equivilence Relations And Classes Problems

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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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  • Text on a white background titled Questions on Equivalence Relations / Classes, stating question 1(a) defining x ~ y when x - y is divisible by m for natural m, and 1(b) defining X ~ Y on the power set of A when the symmetric difference of X and Y is a subset of B, with prove-it instructions.
    problem.JPG
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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