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].

Answer

equivalence class `{0}={2 x}`

Explanation

`{R}=({a}, {b}): 2 / ({a}-{b})`

`Rightarrow(a-b)` is a multiple of` 2 `.

To find equivalence class 0 , put `b=0`

So, `(a-0)` is a multiple of` 2`

`Rightarrow` a is a multiple of `2`

So, In set z of integers, all the multiple

of 2 will come in equivalence
class {0}

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