Hey, I can't seem to get anywhere with this big question so if someone could work through this question with me so I understand that would be greatly appreciated.

a) If give a counterexample to

b) Prove

c) Using part b, prove that if is finite then fixes at least one element

I think for part c that if , I can then pick some and consider for each element .

But I can't get any of part a,b or c anyway.

Thanks guys for any help you can give me.