$$

Q$4.$ Consider a scheduling problem where a university needs to assign professors to teach various courses while satisfying certain constraints. The constraints include:

$$ Each professor can only teach one course at a time.

$$ Each course must be taught by exactly one professor.

$$ Professors have specific preferences for the time slot they would like to teach.

The courses to be scheduled are:

$$ Course A

$$ Course B

$$ Course C

$$ Course D

The available time slots are:

$$ Time Slot $1$

$$ Time Slot $2$

$$ Time Slot $3$

The professors are:

$$ Professor X prefers Time Slot $1.$

$$ Professor Y prefers Time Slot $2.$

$$ Professor Z has no preference.

Question:

Define the Variables, Domains, and Constraints:

a$.$ Define the variables that represent the decision variables for this CSP$.$