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

A group of six friends play some games of ping-pong with these results: Amy beats Bob Bob beats Carl Frank beats Bob Amy beats Elise Carl beats Dave Elise beats Carl Elise beats Dave Frank beats Elise Frank beats Amy Consider the relation R = {hx, yi : x has beaten y}. (a) Draw the directed graph G representing R. (b) Is R reflexive? Irreflexive? Symmetric? Asymmetric? Antisymmetric? Transitive? An equivalence? An order? (c) The players want to rank themselves. Find every possible topological order of G. (d) In order to have a definitive ranking, the players want there to be only one possible topological order. Which two players should face each other? (e) The transitive closure of R (R+), is an order. Is it partial or total?

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Colby Messinger answered 10 months ago

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