$4-(10$ pints$)$ After determining the primary key for your student database, your team is now debating the optimal index type $(\backslash ($ B$+\backslash )$ tree or hashing$)$ to use for the secondary column. Consider the following scenarios:

$-$ Assume you have an effective hashing function that distributes the keys uniformly across the reserved storage space. In this case, which index type would be more beneficial $(\backslash ($ B$+\backslash )$ tree or hashing$)?$ Justify your choice with specific reasons.

$-$ Now assume that a good hashing function is not available, leading to uneven key distribution in the reserved storage space. In this situation, which index type would be preferable $(\backslash ($ B$+\backslash )$ tree or hashing$)?$ Explain your reasoning and the implications of your choice.

In your response, consider factors such as query performance, data retrieval efficiency.

$5-(20$ points$)$ Considering the following B$+$ tree for an index file

A$-$ Show the index after inserting entries with values $6,$ and $36,$ in that order

B$-$ Based on the result of part A$,$ show the tree after deleting $16$