On the set NN define mn approximately kl if 2m 3l 2k 3n I

On the set N*N define (m,n) approximately (k,l) if 2m - 3l = 2k - 3n I_R approximately an equivalent relation.

Solution

if m,n belongs to NxN that means they can get all the positive values

~ this relation means similarly so k,l can take similar values as m,n so the relation (m,n)~(k,l) means they are equivalent

Now , 2m-3l = 2k-3n means for all values of m,n similar values of k,l exist so this I(r) is an equivalence