Imagine a digital library system where different sets represent various collections of books. The library manager uses set operations to manage and analyze these collections. Consider the following sets:

A: Set of all books related to Computer Science.

B: Set of all books related to Mathematics.

C: Set of all books related to Artificial Intelligence.

Using these sets, answer the following questions:

Define each of the following sets using set operations and describe what they represent in the context of the library:

$($a$)$ AUB

$($b$)AB$

$($c$)$ A$-$C

$($d$)(AB)$