Transitivity of a relation on a set. 
My book says the answer is B. But how. I understand that the relation is reflexive as (a,a) belongs to R for all a belonging to the given set. Furthermore I understand that the relation is not reflexive as (a,b) belongs to R does not imply that (b,a) belongs to R for all a,b belonging to the given set. What I don't understand is how is the relation transitive ? I mean they have given (1,3) and (3,2) and (1,2) in the relation which makes it transitive for one case. But doesn't transitivity mean that (a,b) belongs to R and (b,c) belongs to R implies that (a,c) belongs to R for all a,b,c belonging to the given set. Isn't the for all violated here? In transitivity? So shouldn't it be not transitive ? Or am I missing something. 
EDIT 
My book's statement:


For it not to be transitive, you need an a,b,c such that (a,b) and (b,c) are in R, but (a,c) is not (a,b,c need not be different).  Are seeing any instance of this?  Let's see. Here are all pairs of pairs (a,b) and (b,c) in R:
(1,1) and (1,1)
(1,1) and (1,2)
(1,1) and (1,3)
(1,2) and (2,2)
(2,2) and (2,2)
(3,2) and (2,2)
(1,3) and (3,2)
(3,3) and (3,2)
(1,3) and (3,3)
(3,3) and (3,3)
Now, let's see if the (a,c) pair is in R in all those cases as well:
(1,1) and (1,1) => (1,1)  Yes!
(1,1) and (1,2) => (1,2)  Yes!
(1,1) and (1,3) => (1,3)  Yes!
(1,2) and (2,2) => (1,2)  Yes!
(2,2) and (2,2) => (2,2)  Yes!
(3,2) and (2,2) => (3,2)  Yes!
(1,3) and (3,2) => (1,2)  Yes!
(3,3) and (3,2) => (3,2)  Yes!
(1,3) and (3,3) => (1,3)  Yes!
(3,3) and (3,3) => (3,3)  Yes!
Yes, they all are ... so it is transitive.
