I am trying to study binary relations (for myself, it's not an assignment!) I have the set $\{1,2,3,4\}$, and one of the relations in the exercise is $\{(1,3),(1,4),(2,3),(2,4),(3,1),(3,4)\}$.
A relation is called transitive if whenever $(a,b)$ is a member of $R$ and $(b,c)$ is a member of $R$ then $(a,c)$ is also a member of $R$.
Book says it's not a transitive relation. Why?
In given relation we have $(2,3)$, $(3,4)$ and $(2,4)$. ($x = 2$, $y = 3$, $z = 4$)
Observe that you also have (1,3) and (3,1). However you don't have (1,1).