The players on a football team are all weighed on a scale. The scale rounds the weight of every player to the nearest pound. The number of pounds read off the scale for each player is called his measured weight. The domain for each of the following relations below is the set of players on the team. For each relation, indicate whether the relation is: reflexive, anti-reflexive, or neither symmetric, anti-symmetric, or neither transitive or not transitive Justify your answer. (a) Player x is related to player y if the measured weight of player x is at least the measured weight of player y. No two players on the team have the same measured weight.
(b) Player x is related to player y ifthe measured weight of player x is at least the measured weight of player y. There is at least one pair of players on the team who have the same measured weight. There is also at least one pair of players on the team who have different measured weights.
(c) Player x is related to player y ifthe measured weight of player x is at least the measured weight of player y. All the players on the team have exactly the same measured weight