$4$ Big O and Big Omega

$1.$ Consider this pair of functions:

$()=32+$ log $,$

$()=5$ log$2/$ log log $+2.$

Answer the following questions, and provide a justification for your answer in each case.

$($a$)(2$ marks$)$ Is $=\backslash$Omega $()?$

$($b$)(2$ marks$)$ Is $=\backslash$Omega $()?$

$2.(2$ marks$)$ Do there exist functions $,,$ and $$ such that $$ is not big$-$O of $,$ is not big$-$O

of $,$ but $$ is big$-$O of $?$ Justify your answer