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Python Sets

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Set Operations: Symmetric Difference & Difference

5:55 with AJ Tran

The other two main set operations are Symmetric Difference and Difference. These methods allow you to contrast the membership of collections.

Main Set Operations

The following methods and operations return a new set.

s.difference(t) / s - t - Return the difference of two or more sets as a new set. (i.e. all elements that are in this set but not the others.)

s.symmetric_difference(t) / s ^ t - Return the symmetric difference of two sets as a new set. (i.e. all elements that are in exactly one of the sets.)

Additional Notes

The symmetric difference can also be found with the union minus the intersection: (s | t) - (s & t)

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    As I look at our shared ingredients that are common to all five of our omelettes, 0:00
    I think, wow, that's a great basic omelette. 0:05
    I want to update our menu to let customers build their own omelette. 0:09
    They can start with a basic omelette with eggs, onion and cheese. 0:13
    And then they can pick whatever other ingredients they would like as long as we 0:18
    have them. 0:23
    On our Venn diagram, that would be a set of the left and 0:24
    right sides without the middle. 0:27
    I'm looking for the symmetric difference that is all of the ingredients that 0:30
    are not members of the intersection. 0:34
    First of all demonstrate with two omelettes. 0:37
    We'll take the symmetric difference of the vegetarian omelet and 0:44
    the bacon omelet, and print it out to our terminal. 0:49
    The symmetric difference method is a little bit different than the other Venn 0:57
    diagram methods I've demonstrated so far. 1:02
    Watch what happens if I try to pass in more than one argument to 1:05
    symmetric difference with the denver omelet. 1:09
    I get a traceback. 1:15
    It says that symmetric difference takes exactly one argument. 1:17
    And, watch now what happens when I try to 1:22
    chain these methods together with dot notation. 1:24
    We'll comment out line 25, so I don't get that same error again. 1:34
    This time, I do get a set of green pepper, eggs, 1:41
    onion, black olives, ham, bacon and cheese. 1:46
    But if you recall earlier when we got the intersection of our shared ingredients, 1:52
    we know that eggs onion and cheese are common to every omelet. 1:57
    So the symmetric difference really only works for two arguments. 2:02
    It returns a symmetric difference of two sets as a new set, right? 2:07
    This means that we'll have to go about a different way of 2:12
    finding these ingredients that we can put on our custom menu. 2:17
    But before we move on to that, 2:22
    we know that there's a shorthand operator for this as well. 2:24
    And we can still learn that before we move on. 2:28
    So if I wanted to take the symmetric difference, 2:31
    Of the vegetarian omelet, and the bacon omelet, then I can use the caret symbol. 2:38
    And we'll call this different_ingredients. 2:48
    So the different ingredients between the vegetarian and 2:54
    bacon omelettes, are tomatoes, bacon, and black olives, awesome. 2:59
    So one way of finding the set, 3:09
    that is everything except for the intersection. 3:13
    Recall that all ingredients is the union. 3:19
    It's a giant superset of all five of our omelettes. 3:24
    And our shared ingredients is a subset of all of 3:30
    the ingredients that are common to every single omelet. 3:34
    So what we can do here is that we can actually take the union and 3:40
    then subtract the intersection to get the difference of omelets for more than two. 3:46
    That is we can get the difference of all five omelettes, 3:53
    I'll show you what that looks like. 3:57
    We'll call this variable, this new variable called custom_ingredients. 4:00
    And we'll take our other variable, all_ingredients with 4:10
    the difference of these shared_ingredients and we can print that out. 4:15
    In our terminal we've got a lot of ingredients in this set. 4:26
    There's green pepper, tomato, bacon, black olives, spinach, 4:34
    green chili, turkey, ham, avocado, and mushrooms. 4:38
    However, what we don't have is egg, onion and cheese. 4:42
    That's great. 4:46
    So, from the set of all ingredients, we can take away 4:47
    the difference of membership from the set of common ingredients. 4:52
    And instead of dots difference, 4:58
    we can use the shorthand operator which is the minus sign. 5:00
    We'll say custom_ingredients_2 = all_ingredients - shared_ingredients. 5:06
    And we can print(custom_ingredients_2) 5:14
    Nice, these two sets are equal to each other even though I made them in 5:23
    different ways. 5:28
    What I'll do is, 5:31
    I can make a comparison with the double equal sign to prove it programmatically. 5:32
    When I run my script in the console, 5:41
    I should expect to see a boolean value of true. 5:43
    Nice, this is just one of the best things about programming. 5:48
    There's more than one way to accomplish a task. 5:52

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