example verification partial order

Question

Let A= { 1, 2, 3} then R= { (1, 1), (2, 2) , (3, 3) , (1, 2), (2, 3) } ,the relation R is reflexive and anti-symmetric,i get it, but how is it following the transitive property for it to become partial order relation of set A?,really need to clear this up,is it not needed that a partial relation follows the transitive property??

Answer 1

This is NOT transitive because even though (1,2) and (2,3) are in the relation but (1,3) is not in the relation. Hence this is NOT a partial order.