This question is giving me a lot of trouble:

Given the set A = {1, 2, 3} and the set S = {(x, y) | x and y in A}

Consider the relation defined on S as follows: ((x₁, y₁) (x₂, y₂)) if x₁ x₂ and y₁ y₂

Draw the directed graph of this relation. Show that it is a partial order, explain why it is not a total order.

these are my thoughts:

if A x A = {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)}

The set R (relation) would contain all of A x A because (1,1) is less than all other tuples. But that would mean the relation is transitive, reflexive and symmetric, and that does not describe a partial order.

I think I am not understanding how to do this correctly