This problem involves predicate logic and quantifiers. I was able to get some parts of the problem, but when they add the big O part, I really got confused, appreciate the help, thanks!

12 marks Rewrite cach of the following theorems using quantifiers and predicates. Note that the theorems are not precisely stated. It is up to you to choose reasonable sets from which the variables should be drawn. Further, notice that the definitions we have given you should be stated as predicates, but we would like you to formalize their specification. Make sure that your theorems have no unbound variables. 4 marks] We define "big-O" as follows: Theorem: Let k be a constant. If f(n) 0(h(n)) then k . f(n) 0(h(n))