Hey there,

I had an exam question on this the other day! To show that 1.,2. imply 3. on it's easiest to show it for first, then , and then . I'll give you some hints!

(n)Try induction to show that . This is obvious for , and so assume it is true for . Then From here you can use 1. and the inductive hypothesis. The symmetric case, i.e. for follows from 2.

(z)Then for , it suffices to show that (why?). Consider and use 1. Again use 2. for the symmetric case.

(q)Now for , it suffices to show (why?). Now consider and use(n).

Hope this is helpful, write back if you get stuck

(I don't know why I just used a smiley I think they're stupid but I was endeared by the yellowness.)