Welcome to today's lesson! We'll be exploring a practical application of Python sets by managing student enrollments for various courses. Imagine you're running an online course platform and need to handle enrollments, checks, and listings of students in different courses. Sets would be perfect for this kind of problem since they don’t allow duplicates, ensuring that a student can't enroll in the same course more than once!

By the end of this session, you'll be well-versed in using sets for such tasks. Let’s dive in!

Here are the methods we need to implement in our enrollment system:

• enroll(self, student: str, course: str) -> None: This method adds a student to a course. If the student is already enrolled, it does nothing.
• unenroll(self, student: str, course: str) -> bool: This method removes a student from a course. It returns True if the student was enrolled and has now been removed. Otherwise, it returns False. If after unenrolling the student, the course becomes empty (no one is involved there), remove the course as well.
• is_enrolled(self, student: str, course: str) -> bool: This method checks if a student is enrolled in a course. It returns True if the student is enrolled and False otherwise.
• list_students(self, course: str) -> list[str]: This method returns a list of all students enrolled in a given course. If no students are enrolled, it returns an empty list.

Let's look at how to implement each of these methods step-by-step.

We'll start by defining our class and then add each method one by one.

First, we define our EnrollmentSystem class:

class EnrollmentSystem:
    def __init__(self):
        self.enrollments = {}

This code initializes an EnrollmentSystem class with a dictionary named enrollments that maps courses to sets of students.

Next, we implement the enroll method:

class EnrollmentSystem:
    def __init__(self):
        self.enrollments = {}

    def enroll(self, student: str, course: str) -> None:
        if course not in self.enrollments:
            self.enrollments[course] = set()
        self.enrollments[course].add(student)

# Example usage:
es = EnrollmentSystem()
es.enroll("Alice", "Math101")
print(es.enrollments)  # Output: {'Math101': {'Alice'}}

Here, the enroll method checks if the course exists in the enrollments dictionary. If it doesn't, it initializes a new set for that course. Then, it adds the student to the set of students for that course.