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Python Python Collections (2016, retired 2019) Sets Set Math

Posted by Zach Widhalm
Zach Widhalm
6,406 Points

Difference between intersection and subset?

I know the attached code works with intersection instead of subset, but could someone explain why? Maybe my understanding of the two are incorrect but I figured if the passed in argument was a subset of the values, the list would be appended with the key. Thanks!

sets.py 
COURSES = {
    "Python Basics": {"Python", "functions", "variables",
                      "booleans", "integers", "floats",
                      "arrays", "strings", "exceptions",
                      "conditions", "input", "loops"},
    "Java Basics": {"Java", "strings", "variables",
                    "input", "exceptions", "integers",
                    "booleans", "loops"},
    "PHP Basics": {"PHP", "variables", "conditions",
                   "integers", "floats", "strings",
                   "booleans", "HTML"},
    "Ruby Basics": {"Ruby", "strings", "floats",
                    "integers", "conditions",
                    "functions", "input"}
}

def covers(arg):
    list = []
    for keys,values in COURSES.items():
        if arg.issubset(values):
            list.append(keys)
    return list

1 Answer

Brandon Spangler
Brandon Spangler
8,756 Points
Brandon Spangler
Brandon Spangler
8,756 Points

I think your confusion stems from a lack of understanding the difference between a subset and the intersection of two sets. An intersection between two sets is all the elements the sets have in common. For example, let's say we have two sets, A = {1,2,3,4,5,6,7,8,9} and B = {1,3,5,7,9, 100}. The intersection of these two sets is 1,3,5,7,9. A subset is probably best defined using examples. An example of a subset of set A from above would be {1,2,3} or {1} or {3,7,9} or even {1,2,3,4,5,6,7,8,9}, but set B is NOT a subset of set A because B contains a number that's not in set A. So, the reason intersection works is because we're looking for keys in COURSES whose corresponding set in COURSES.values() has an element that is shared in the set arg. EX: if arg is {"booleans","coffee cup"} then we want our function to return ["Python basics","Java Basics", "PHP basics"] because the intersection between arg and COURSES.values() is {"booleans"}. Now if we had used the subset function, our function would have returned [] because arg is not a subset of any of the sets in COURSES because arg contains an element that is not in the sets in COURSES, namely "coffee cup". However, if arg is just {"booleans"}, then {"booleans"} is the intersection of the two sets and arg is also a subset of some of the sets in COURSES.

I hope that cleared things up a little.

Zach Widhalm
Zach Widhalm
6,406 Points

Thanks for taking the time to type all that up! Much appreciated!

Brandon Spangler
Brandon Spangler
8,756 Points
Brandon Spangler
Brandon Spangler
8,756 Points

My pleasure! Hopefully it helped!