With explanation please.

[8] 4. For any two real numbers r and y, everyone knows that exactly one of r y" must hold. In class we said that f EN(g) is analogous to f > 9", and f E 0(g) is analogous to fo such that f & N(g) and f&o(g)? Prove your solution. [4] (b) Do there exist functions f,g:NRo such that fel(g) and f EO(g)? Prove your solution. Remarks. You should not use the limits definition of Big-O. Also, note that f and g cannot evaluate to 0