I need to show that relation R is partial order relation.

$\displaystyle R = \{ (a,a),(b,b),(c,c),(a,b),(a,c),(b,c)\} $

I see that it is reflexive and transitive, but I don't see that is antisymmetric.

In the book stands that it is antisymmetric because

$\displaystyle (a,b) \in R \wedge (b,a) \notin R$,$\displaystyle (a,c) \in R \wedge (c,a) \notin R,(b,c) \in R \wedge (c,b) \notin R$

Can someone explain me this?