$$A = \{1, 2, 3, 4\}$$

Is the relation `x > y` on $A$ transitive?

If yes please explain why it is so.

There will be the pair `(2,1)` as 2 > 1. However `y` being 1 will have no other pair (y,z) as 1 is the smallest number in the set $A$. So the condition
for the relation to be transitive:

$\forall x,y,z \in A : x R y \land y R z \implies x R z$. 

will return false as there will be no $y R z$ pair to satisfy the whole condition.

Is my thinking right?