For the following relations on the set of POSITIVE integers, determine if it satisfies each of the following conditions: m~ n 19 divides m - n m~n 13 divides m + n 13 divides mn m~ n Reflexive Please enter Y or N in each of the boxes. Symmetric Transitive Equivalence Relation

Relation is defined on positive integer

m~n <=> 19 divide m-n 

Since m-m=0 and 19 divide 0

so m~m => Relation is reflexive 

m~n then 19 divide m-n 

n need not related to m 

Since n-m need not to be positive integer

Relation  is not symmetric

Now let m~n and n~p 

=> 19 divide m-n and 19 divide n-p 

=> m-n=19k , n-p=19l

So m-n+n-p=19(k+l)

    => m-p =19(k+l)

19 divide m-p so m~p 

Relation is transitive

Since Relation satisfy Reflexive, but not symmetric and transitive so the relation is not an Equivalence relation