I have two related problems. Prove or disprove:
If and are transitive relations then is a transitive relation.
If and are transitive relations then is a transitive relation.
The first, I completely understand, because if you union two transitive relations, the combined relation will still be transitive. (Unless I am way off.)
The second has proven more difficult to prove/disprove. Every example that I have come up with has been "vacuously" transitive. I had never heard of that until the other day and I believe that is why it is proving more difficult for me. If anyone could help with this proof, I would much appreciate it. A good nudge in the right direction?
Thanks!
Transitivity is whenever aRb and bRc, then aRc. How would I start a proof that would encompass all situations. I understand how to prove a certain given situation... It is the general proof when I am dealing with X number of terms that confuses me. I cannot just use aRb... I would continue with another line saying something like .
By the way your explanations have helped immensely!