Prove that (a,b)^u = a^u * b^u for all cardinalities a,b, and u
also prove that if a <= b , then a^u <= to b^u
how do you prove these facts? I have no idea how to start the prove
You have posted this same question twice: double posting.
That is against the rules. But I am going to break them and answer.
I can almost be sure that I and no one else has tried to answer is due to one reason.
Here it is.
I have taught this from several different textbooks.
I now have before me three of those textbooks.
Looking at the approaches to your question in those books, to the untrained would seem to have nothing to do with one another. BUT they are the same; the notation changes.
Not only does notation change from textbook to textbook, lecturers change the presentations to suit themselves, I certainly have.
So here it is for you: we simply do not know which of the very may approaches you are required to use. If I gave you mine, the chances are good it would wrong.