How could I prove the transitiveness of the asymmetric part of the transitive relation? Solely for the learning purposes I want to prove it using just set language, while I know how to prove it using graph and analytic languages.
Here are the only notions I want to use:
Here are the conditions of the thing I want to prove:
Here is my first step of proving that:
Why am I asking for the help? I do it because my set language skills are very poor and I would like to develop them, but I can not tackle the issue I faced here on my own.
Will be grateful for any help provided.
Assume R transitive, aRb, bRc, not bRa, not cRb,
Then aRc. If cRa, then bRa a contradiction.
Thus not cRa.
In conclusion, if R is transitive, so is $R^a.$
Use of images does cause delays and no responses.
Graphs, ie diagrams, are never a proof.
What is an analytic language?