$(25$ points$)$ For each pair of expressions $($A$,$ B$)$ below, indicate whether A is O$,\backslash$Omega $,$ or $\backslash$Theta of B$.$ Note that zero, one, or more of these relations may hold for a given pair. List all applicable relations. No explanation is needed. If A $=\backslash$Theta $($B$)$ then write A $=\backslash$Theta $($B$)$ which already implies thatA$=$O$($B$)$andA$=\backslash$Omega $($B$).$ IfA$=\backslash$Theta $($B$)$andyouwriteA$=$O$($B$)$ or A $=\backslash$Omega $($B$)$ only, you will only receive partial credits. It often happens that some students will get the directions wrong, so please write out the relation in full, i$.$e$.,$ A $=$ O$($B$),$ A $=\backslash$Omega $($B$),$ or A $=\backslash$Theta $($B$)$ and not just O$($B$),\backslash$Omega $($B$)$ or $\backslash$Theta $($B$).$