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A group of six friends play some games of ping-pong with these results: Amy beats Bob...

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Advance Math

A group of six friends play some games of ping-pong with theseresults: Amy beats Bob Bob beats Carl Frank beats Bob Amy beatsElise Carl beats Dave Elise beats Carl Elise beats Dave Frank beatsElise Frank beats Amy Consider the relation R = {hx, yi : x hasbeaten y}. (a) Draw the directed graph G representing R. (b) Is Rreflexive? Irreflexive? Symmetric? Asymmetric? Antisymmetric?Transitive? An equivalence? An order? (c) The players want to rankthemselves. Find every possible topological order of G. (d) Inorder to have a definitive ranking, the players want there to beonly one possible topological order. Which two players should faceeach other? (e) The transitive closure of R (R+), is an order. Isit partial or total?

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