Consider the function f $($n$)=$ n $($n mod $2)+$ log n$.$

$($a$)$ Show that f $($n$)$ in O$($n$)$ and f $($n$)$ in $\backslash$Omega $($log n$).$

$($b$)$ Show that neither f $($n$)$ in $\backslash$Theta $($n$)$ nor f $($n$)$ in $\backslash$Theta $($log n$).$

$($c$)$ Suppose for some function g$($n$),$ we have f $($n$)$ in O$($g$($n$)).$ Is it always true that f $($n$)$ in

$\backslash$omega $($g$($n$))?$ Justify your answer with either a proof or a counter$-$example.