I am examining transitive relationships and understand the premise that if $x \rightarrow y \rightarrow z$, then the relation needs to contain $x \rightarrow z$ to be considered transitive. My questions was if I had the relation $A = {(1,2), (2,3), (3,4), (4,5)}$, does including $(1,5)$ make this a transitive relation or would I need also ${(1,3),(1,4),(1,5)}$. If the latter is the case, would I need furthermore to add to the relation for a transitive relation: ${(2,4),(2,5),(3,5)}$?
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1Yes. You would need all of those additional elements to make the relation transitive. – John Douma May 18 '20 at 03:34
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Perfect! Thank you for helping the understanding @JohnDouma – anothercoderbro May 18 '20 at 03:57
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Is $x \rightarrow y \rightarrow z$ supposed to mean something? – William Elliot May 18 '20 at 16:06
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It is required to always proof read your posts which you obviously do not do for if you did you would have seen that A is not a set. Thank Mathjax for that. Edit your post accordingly. – William Elliot May 18 '20 at 16:12
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Pretentious people like yourself are what ruins sites intended for learning and understanding. – anothercoderbro May 18 '20 at 17:18