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.

On the set N of all natural numbers,a relation R is defined as follows: AA n,m in N,nRm 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.

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

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

The relation R defined in the set N of natural number as AAn,minN if on division by 5 each of the integers n and m leaves the remainder less than 5. Show that R is equivalence relation. Also obtain the pairwise disjoint subset determined by R.

Let R={(m,n):2 divides m+n} on Z. Show that R is an equivalence relation on Z.

Let N be the set of all natural numbers and R be the relation in NxxN defined by (a,b) R (c,d), if ad=bc. Show that R is an equivalence relation.