$($a$)$ Add successive nodes with keys $48\mathrm{.}8\mathrm{.}69.7\mathrm{.}50.52.71.1/23/10$ into an empty binary search

tree. Document the condition after each insertion operation. Is the resulting tree

a red black tree? If yes, color it$,$ if no$,$ briefly explain why.

$($b$)$ Let $a,b$ and $c$ be arbitrary nodes from the respective subtrees $A,B$ and $C^{\text{'}}$ in the following binary search tree $T$ :

Next are d$..$ d$.$ d$.$ the depths of the three nodes. Determine the new depths of the three nodes using the

rotateRight$(,$