Transitive binary Relation on sets

Question

Consider a set , A = { 1 , 2 , 3 }

  Subset = { (1,3) , (1,2) } 

is a transitive relation . But I don't get that how it is transitive relation because there is no ordered pair whose first member is 3 .

Answer 1

Transitive means that $xRy\wedge yRz \Rightarrow xRz$.

In your example, the premise $xRy \wedge yRz$ is not fulfilled and so the relation is transitive.

In case of $R=\{(1,2),(2,3)\}$, the relation would not be transitive, since the premise holds, but $(1,3)$ is missing in $R$.