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+"""CSC110 Fall 2021 Assignment 1, Part 2: Programming Exercises
+
+Instructions (READ THIS FIRST!)
+===============================
+
+Note: these instructions are essentially the same as Prep 2, so we strongly recommend
+completing the Prep 2 Programming Exercises first before starting this part.
+
+This Python module contains the functions you should complete for Part 2 of this assignment.
+Your task is to complete this module by doing the following for EACH function below:
+
+1. Add a new doctest example to the function description in the space provided.
+   This will ensure you understand what the function is supposed to do.
+   (You may add more than one doctest for testing purposes if you wish.)
+2. Write the body of the function so that it does what its description claims.
+
+In some function descriptions, we have written "You may ASSUME..." This means that
+when you are writing each function body, you only have to consider possible values
+for the parameters that satisfy these assumptions.
+
+By the way, we *will* be checking that you've added new doctest examples, and that
+your examples correctly illustrate a call to that function. Don't skip this!
+
+For instructions on checking your work with both doctest and python_ta, please check
+the assignment handout.
+
+Copyright and Usage Information
+===============================
+
+This file is provided solely for the personal and private use of students
+taking CSC110 at the University of Toronto St. George campus. All forms of
+distribution of this code, whether as given or with any changes, are
+expressly prohibited. For more information on copyright for CSC110 materials,
+please consult our Course Syllabus.
+
+This file is Copyright (c) 2021 David Liu, Mario Badr, and Tom Fairgrieve.
+"""
+import math
+
+
+def find_roots_quadratic(a: float, b: float, c: float) -> set:
+    """Return a set containing the solutions to the equation ax^2 + bx + c = 0.
+
+    Each solution is a float.
+
+    You may ASSUME that:
+      - a != 0
+      - (b * b) - (4 * a * c) >= 0
+
+    >>> find_roots_quadratic(1, -15, 56) == {8.0, 7.0}
+    True
+    >>> find_roots_quadratic(1, -10, 21) == {3.0, 7.0}
+    True
+    >>> find_roots_quadratic(1, 8, 15) == {-3.0, -5.0}
+    True
+    >>> # Have to use isclose to compare floats
+    >>> all([math.isclose(sol, -0.739, abs_tol=0.001) or math.isclose(sol, 1.739, abs_tol=0.001) for sol in find_roots_quadratic(7, -7, -9)])
+    True
+
+    Hint: use the quadratic formula.
+    """
+    assert a != 0
+    assert (b * b) - (4 * a * c) >= 0
+    part = math.sqrt(b * b - 4 * a * c)
+    return {(-b - part) / (2 * a), (-b + part) / (2 * a)}
+
+
+def intersect_all(set1: set, set2: set, set3: set) -> set:
+    """Return the intersection of all three of the given sets: set1, set2, and set3.
+
+    >>> intersect_all({1, 2, 3}, {1, 2, 3, "test"}, {1, 2, 6, 7, "test"}) == {1, 2}
+    True
+    >>> intersect_all(set(), {1, 2, 3}, {1, 2, 3}) == set()
+    True
+    >>> intersect_all({"a", ""}, {1, 0}, {True, False}) == set()
+    True
+    >>> intersect_all({'a'}, {"a"}, {chr(97)}) == {'a'}
+    True
+    """
+    return set.intersection(set1, set2, set3)
+
+
+def greet_all(greeting: str, names: list) -> list:
+    """Return a list of strings that consist of the greeting messages for each person in names.
+
+    The format of each greeting message is '<greeting>, <name>',
+    where greeting is the given greeting and <name> is an element of <names>.
+
+    The returned list should contain the greetings for the names in the same order each name
+    appears in the given names list.
+
+    You may ASSUME that:
+        - names is either empty or contains elements that are strings
+
+    >>> greet_all('Good morning', ['Alan Turing', 'Grace Hopper'])
+    ['Good morning, Alan Turing', 'Good morning, Grace Hopper']
+    >>> greet_all('', [])
+    []
+    >>> greet_all('<greeting>', ['<name>'])
+    ['<greeting>, <name>']
+    >>> greet_all('', ['', ''])
+    [', ', ', ']
+    """
+    # assert all([isinstance(name, str) for name in names])
+    return [f'{greeting}, {name}' for name in names]
+
+
+def all_smaller(nums1: set, nums2: set) -> bool:
+    """Return whether every number in nums1 is less than every number in num2.
+
+    You may ASSUME that:
+      - nums1 is non-empty
+      - nums2 is non-empty
+      - nums1 and nums2 contain only integers and/or floats
+
+    >>> all_smaller({2}, {3})
+    True
+    >>> all_smaller({3}, {2})
+    False
+    >>> all_smaller({2, 3}, {2, 3})
+    False
+    >>> all_smaller({1, 2, 3}, {4, 5, 6})
+    True
+    >>> all_smaller({-100, -101}, {-1, 0})
+    True
+    >>> all_smaller({0.11}, {0.1})
+    False
+    >>> all_smaller({-0.01}, {-0.009})
+    True
+
+    Hint: use the min and max functions.
+    """
+    assert len(nums1) != 0
+    assert len(nums2) != 0
+    return max(nums1) < min(nums2)
+
+
+if __name__ == '__main__':
+    import doctest
+    doctest.testmod(verbose=True)
+
+    # When you are ready to check your work with python_ta, uncomment the following lines.
+    # (Delete the "#" and space before each line.)
+    import python_ta
+    python_ta.check_all(config={
+        'extra-imports': ['math'],
+        'max-line-length': 100
+    })