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Let R be the relation in the set Z of in...

Let R be the relation in the set Z of integers given by R={(a,b):2 divides a-b}. Show that the relation R transitive ? Write the equivalence class [0].

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Let 2 divides `(a-b)` and 2 divides `(b-c)` : where `a,b,c, in Z`
So 2 divides `[(a-b)+(b-c)]`
2divides `(a-c)` : Yes relation R is transitive
`[0]={0,+-2,+-4,+-6,....}`
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