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I know that at first this sounds like a stupid question but I'm not sure about its meaning.

Transitivity states that whenever $(a,b) \in R$ and $(b,c) \in R$, then $(a,c) \in R$, where R is the relation.

Take for example the elements $a=1, b=2$. Now, $1$ is in relation to $2$, so to test for transitivity I'd need a pair $(2,c) \in R$. However, I don't have any pair that satisfies that condition so I'm not sure how to proceed from here. If I had a pair $(2,c)$, I could easily check whether transitivity holds for $1$ if simply $1Rc$. However, since I can't do that, I'm not sure if this relation is transitive or not.

bb_823
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THE_CRANIUM
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    Since $(2,c)\in R$ never holds, $$(1,2)\in R\text{ and }(2,c)\in R\implies (1,c)\in R$$ is true for all $c$. – Surb Jul 08 '23 at 08:50
  • @Surb so generalizing it for all elements of $A$, $R$ is transitive? – THE_CRANIUM Jul 08 '23 at 09:07
  • Yes it is transitive. – Surb Jul 08 '23 at 09:30
  • From How to ask a good question: "Your question should be clear without the title. After the title has drawn someone's attention to the question by giving a good description, its purpose is done. The title is not the first sentence of your question, so make sure that the question body does not rely on specific information in the title." – jjagmath Jul 08 '23 at 10:26

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