On the set N of all natural numbers, a relation R is defined as follows: `AA n,m in N, n R m` Each of the natural numbers `n` and `m` leaves the remainder less than 5.Show that R is an equivalence relation. Also, obtain the pairwise disjoint subsets determined by R.

Explanation

Reflexive

`a in N`

`aRa`

Symmetric

`a,b in N`

`aRb->`remains=0,1,2,3,4.

`bRa`->remains=0,1,2,3,4.

Transitive

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