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- Show that the relation R defined by R={(a,b):a-b is divisible by 3;a,b E N}is an equivalence relation .

**Reflexivivity**: For any , we have

Thus, for all . So, R is **reflexive**.

**Symmetricity**: Let .

Thus, for all . So, R is **symmetric**.

**Transitivity**:Let such that and . Then,

So, R is **transitive**.

Thus, R is an **equivalence relation**.

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