Let R = {(a, b): a, b e Z and (a – b) is divisible by 5).
Show that R is an equivalence relation on Z.
the set A – 11​

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1. Answer:

   Given:

   R={(a,b):a,b∈Z and (a−b) is divisible by 5}.

   R=(a,b)

   (a−b) is divisible by 5

   Reflexive

   (a,a)⇒(a−a) is divisible by 5

   Symmetric

   (a,b)⇔(b,a)

   (a−b) is divisible by 5

   (b−a) is divisible by 5

   Transitive

   (a,b),(b,c)⇔(a,c)

   (a−b) is divisible by 5

   (b−c) is divisible by 5

   (a−c) is divisible by 5

   R is an equivalent relation on Z

   Explanation:

   hope it is help you

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