Hello (1st post!).
I've been having a bit of trouble with this assignment question. I think i've done it right, but when you have 3 questions asking for a "true or false" answer, you'd expect at least one of them to be true!
It's parts iiia), b) and c). (the parts with F? next to them. I've also posted what N and N** are further down the page)
My answer to parts a) and b) are:
(for part b), "curly N" (or N as i'll write) is just the usual addition and multiplication in the natural numbers. N** is similar, but with an alpha and beta added in (ordinals?). Here's what the book says:
Finally, my answer to part c is:
As you can see, i've followed a similar method every time. Since the formula is valid "for all x there exists y", it was my plan to find a y for some x so that it isn't true. Unfortunately, it seemed quite easy to find a counter example each time.
Am I right? It would be stellar for someone to either back me up!