$4.$ Convert the following "data" dictionary into DataFrame df representing a student record

data $=\backslash \{$ 'StudentID': $[101,102,103,104,105,106],$ 'Name': $[\text{'}$Alice$\text{'},$ 'Bob', 'Charlie', 'David', 'Eve', 'Frank'$],$ 'Math': $[85,70,90,65,95,88],$ 'English': $[78,82,88,75,92,80],$ 'Science': $[92,81,85,89,78,85],$ 'History': $[75,85,82,80,70,88]\backslash \}$

Execute the following code after you create the dataframe $\text{'}$ df $\text{'},$

df$.$set$\_$index$(\text{'}$StudentID$\text{'},$ inplace$=$True$)$

Perform the following tasks below using Index operations and methods. $(25$ points$)$

a$.$ Add a new index pd$.$Index $\backslash (([107,108])\backslash )$ to the df$.$index, representing two additional student IDs. Show the updated Index and note the resulting Index structure.

b$.$ Create a new Index pd$.$Index $\backslash (([101,103,107])\backslash )$ and find the difference between df$.$index and this new Index. List any student IDs that exist in the original DataFrame Index but not in the new Index.

c$.$ Create another Index pd$.$Index $([102,103,106,108]).$ Find the intersection and union of df$.$index and this new Index. Print the resulting Indexes.

d$.$ Using the original df$.$index, check if each student ID is part of pd$.$Index$([101,105,107,109]).$ Display the Boolean array resulting from this operation.

e$.$ Remove the student with ID $104$ from the Index. Show the updated Index and confirm the deletion.

f$.$ Insert a new student ID $110$ at position $3$ in df$.$index. Display the modified Index.

g$.$ Determine if df$.$index is unique and if it is monotonically increasing. Provide a Boolean result for each.

h$.$ Print the unique values in the df$.$index and explain if any duplicates were found.