Subject: Games and Decision Making in Data Analysis
Consider 5 famous heavyweight professional boxers Mike Tyson, Lennox Lewis, Evander Holyfield, Vitali Klitschko and Hasim Rahman:
a Evander Holyfield—Mike Tyson, November 9, 1996. Holyfield won in 11th round with technical knockout.
b Evander Holyfield — Mike Tyson, June 28, 1997. Tyson was disqualified for two bites of the Holyfield’s ears.
c Lennox Lewis — Evander Holyfield, March 13, 1999. Draw.
d Lennox Lewis — Evander Holyfield, November 13, 1999. Lewis won on points.
e Hasim Rahman — Lennox Lewis. April 22, 2001. Rahman won by knockout in the 4th round. f Lennox Lewis — Hasim Rahman. November 17, 2001. Lewis won by knockout in the 5th round. g Evander Holyfield — Hasim Rahman, June 1, 2002. Holyfield won on points after the fight was stopped in the 8th round. h Lennox Lewis — Mike Tyson, June 8, 2002. Lewis won by knockout in the 8th round. i Lennox Lewis — Vitali Klitschko, June 21, 2003. Lewis won by technical knockout in the 6th round.
Consider on the set of these athletes a binary relation: xP y if and only if boxer x has defeated boxer y at least once. Construct the graph of this binary relation. Check whether P is reflexive, irreflexive, connected, symmetric, asymmetric, transitive, negatively transitive binary relation. Does this binary relation satisfy semitransitivity and strong intervality condition? Explain your answer (prove, if it is true, or provide a counterexample, if it not true).
