The players on a football team are all weighed on a scale. The scale rounds the

Question

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 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. Player x is related to player y if the 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. Player x is related to player y if the 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.

Explanation / Answer

a) As no players on the team have the same measured weight that means it is not reflexive so it is antireflexive. Further if x is atleast the measured weight of player y then y should not have atleast the measured weight of player x, so it is also antisymmetric But if x is atleast the measured weight of player y and player y is atleast the mesured weight of z, then surely x is atleast the measured weight of player z. So it is transtive relation here.

This is the answer of part (a)

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(b) It is reflexive as here atleast one pair of players have the same weight measured. But it is again antisymmetric as if x is atleast the measured weight of player y then y should not have atleast the measured weight of player x, so it is also antisymmetric. But if x is atleast the measured weight of player y and player y is atleast the mesured weight of z, then surely x is atleast the measured weight of player z. So it is transtive relation here.

This is the answer of part (b)

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(c) It is only the reflexive relation as both elements of concerned ordered pair have same elements. So it is reflexive, but neither symmetric nor transitive.

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