Given the following relation, { ( A, A ), ( A, B ), ( A, D ), ( B, B ), ( B, C ), ( B, E ), ( C, B ), ( C, C ), ( C, D ), ( D, A ), ( D, B ), ( D, C ), ( D, E ), ( E, D ), ( E, E ) }
i) Draw the digraph of the relation,

ii) construct the matrix diagram for the relation,

and iii) why or why not is the relation reflexive, symmetric, antisymmetric, transitive?

Let U = Z⁺ ? { 0 }.
Let R₁ = { ( x, y ) | x < y }
Let R₂ = { ( x, y ) | x > y }
Let R₃ = { ( x, y ) | x ? y }
Let R₄ = { ( x, y ) | x ? y }
Let R₅ = { ( x, y ) | x ? y }
Let R₆ = { ( x, y ) | x = y }
Find:
a) R₂ ? R₃
b) R₂ ? R₄
c) R₄ ? R₅