Question

Question 5# Teams P.Q.RST and each play. every other team once at home and once away. The results for the home team in each match are displayed in the table at right. For example S defeats Q at home but loses to Q away. There are no drawn matches. Relations α, β and γ | OIT on the set of six teams are defined below. Draw a (directed) graph for each relation and say whether V or not the relation is a function. If it is not a function, say why not. Away WWW TWW WLW U W L W L W a) ray defeats y at home and lose s to y away (b) xßy +> x defeats y away and loses to y at home (c) x y x defeats y both at home and away Draw your graphs in a similar way to the example at right which is for the relation δ on the set of six teams, where roy means that x loses both matches against y.

Answer 1

Ces-5 Teams P.aR.S,T and each Pa eveey other team once at home and o auday The tesults o the home am in each Małch are displayed in the. able at jght Criven "Thatラ nce x ay *> x defeats y at home and loses b) xpy defeats y away and loses to edePeats y both at hame 4 dway at home and auway Solv כ at home and loses to y is not a functiona awda depeats This grap have a bi direchiona rphn thi which Cannot be a Punction

This araph is also not a function because is also bidirected This graph is a Punction due to its unidirectional r is a unction due to