Which of the following is not an equivalence relation on set of intergers

If R has to be reflexive then for all a∈N ,a has to be less than a itself that is a<a which is not possible. So R is not reflexive.$$$$
If R has to be symmetric then for all a,b∈N  or a<b⇒b<a but we see that if a>b then we cannot have b>a. So R is not symmetric.$$$$
 If R has to be transitive then for all a,b∈N a<b,b<c⇒a<c which is true because the natural number set N is an ordered set. So R is transitive.