Prove that P( ) and Q( ) are both different from O( )—that is, we can’t just use either of the new definitions without changing what we meant. Specifically, prove that there exist functions f and g...

Prove that P( ) and Q( ) are both different from O( )—that is, we can’t just use either of the new definitions without changing what we meant. Specifically, prove that there exist functions f and g such that .

1. . . either (i) f = O(g) but f 6= P(g), or (ii) f 6= O(g) but f = P(g).

2 . . . either (i) f = O(g) but f 6= Q(g), or (ii) f 6= O(g) but f = Q(g).