Suppose that is transitive on .
Suppose that .
By definition .
But that means that because is transitive.
So by way of we have .
Can you extend that to
Let be a transitive relation defined on a set . Prove or disprove that is a transitive relation.
I'm inclined to believe that it's true, but I can't be sure. I at least know this: A relation is transitive on a set if whenever and , then ,