prove the relation a=L(mod m) is aequivalent relation?
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Expert's answer
2011-11-29T08:55:49-0500
to prove we must show that this relation is reflexive, symmetric and transitive reflexive: a=a( mod m) it is obvious statement by the definition of mod m symmetric if a=b(mod m) then b=a (mod m) to prove this we can write if a=b(mod m) then a have the same remainder after division by m as b. so b have the same remainder after division by m as a so b=a(mod m) transitive: if a=b(mod m) and b=c(mod m) then a=c(mod m) . if a=b (mod m) so a have reminder after division by m and its equal to the same remainder of b , from b=c(mod m) we have that b have reminder after division by m and its equal to the same remainder of c. so a and c have the same remainder . so a=c(mod m)
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