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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...
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
