Let X 1 2 34 Present the digraph of a binary relation p on

Let X = {1, 2, 3,4}. Present the digraph of a binary relation p on X such that rho is antisymmetric and also the digraph for rho has the maximum possible number of edges (a directed edge from a vertex to itself also counts)? Let X = {1, 2,...,n) and p be a binary relation on X such that p is antisymmetric. Show that the maximum number of directed edges that the digraph can have (a directed edge from a vertex to itself also counts) is n(n+1)/2.(Do not show the digraph but just provide a justification.)

Solution

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