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**carla1985** OK, so I have managed to prove a couple of partial orders already so understand the reflexive, anti-symmetric and transistive properties to some degree but this question has really thrown me, especially for the latter two properties. Could someone please help me out. Thanks x

Let X = {1,2,3} and let Y be the set X2 consisting of all pairs Y ={(x1, x2) : x1, x2 ∈ X}. So, e.g., Y consists of things like (3, 1), (1, 2), (3, 3).

Define a relation on Y by (x1,x2)R(x′1,x′2) if and only if the followinghold: Either (x1 < x′1) or (x1 = x′1 and x2 ≤ x′2). (Where < is the usual “lessthan” relation on the integers 1, 2, 3).

Prove that this relation is a partial order on Y . Draw its Hasse diagram.Is this also a total order, or not?