Transitive and also reflexive chart

  1. The solution for this becomes just irreflexive. Nonetheless, just how is this not transitive? The definition I have for transitive states "whenever there is a course from x to y after that there have to be a straight arrowhead from x to y". So for the above chart, if there exists a course from one indicate an additional, after that there need to be a straight arrowhead. Well that seems the instance for the above photo, no? Theres a course from C to B, and also there is a straight arrowhead. There is no course from C to E, so no arrowhead required. No course from B to C, B to D, so no arrowheads required below. There is a course from Z to An and also there is additionally a straight arrowhead, and also very same for A to Z. Am I misconstruing this?

  2. The Wikipedia article for transitive relation claims :

For a transitive relationship the adhering to are equal :

  • Irreflexivity
  • Asymmetry
  • Being a rigorous partial order

Does this mean that if a relationship is transitive, after that it is additionally irreflexive? If thats the instance, after that should not the above chart after that be transitive?

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2019-12-02 02:54:30
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Answers: 1

However, just how is this not transitive?

There is a side from Z to An and also one fully, yet no side from Z to itself or from A to itself.

Does this mean that if a relationship is transitive, after that it is additionally irreflexive?

No, it suggests that if a transitive relationship is irreflexive, it is additionally crooked and also a rigorous partial order (and also if it is crooked, it is additionally irreflexive etc).

So if the chart was transitive, its irreflexivity would indicate that it is additionally antisymmetric, yet given that the chart is not transitive, this does not use.

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2019-12-03 04:25:30
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