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Set Membership & Relationship

11:03 with AJ Tran

Membership testing is a distinguishing feature of sets. Testing for membership means asking if an element is present in a set. Sets can have relationships with each other based on their mutual membership.

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These operations return a boolean value.

Testing for Membership

x in set True if set contains element.

x not in set True if set does not contain element.

Testing for Equality

== "equal to" - True if two sets are equal length and contain the exact same members

!= "not equal to" - Opposite of "equal to"

Testing for Relationship

isdisjoint() - True if two sets have a null intersection (ie. no members in common).

issubset() / <= - True if another set contains this set.

issuperset() / >= True if this set contains another set.

An empty set is both a disjointed set and a subset of all sets.

A set is both a subset and a superset of itself.

Extra Credit

The string module has constants that are good for working with strings. Python has a lot of built-in modules that are very useful to know. You may be familiar with some already, like random, time, or statistics. These modules are part of the Python Standard Library. Modules are vital to know about because it's code that other people wrote to handle common patterns and problems in programming. And you get these for free just by having Python installed on your computer! You can view an index of the built-in modules in the Python documentation

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The concept of membership is a distinguishing feature of sets. 0:00

Recall that an element of a set is called a member. 0:05

The concept of membership testing means asking whether or 0:09

not an element is a member of a set. 0:13

In our last video, we performed membership testing by using the in keyword. 0:17

We can also use the not in keywords to test for non-membership. 0:23

And the answer is a boolean value, true or false. 0:28

Is it there or not? 0:33

Membership testing can be performed on one set. 0:36

When there are two or more sets, membership testing can help us 0:39

determine how different sets are related to each other. 0:44

For example, what happens when all of the members of 0:48

one set are also members of another set? 0:52

A, E, I, O, and U are members of the set of vowels and 0:56

also members of the set of letters of the English alphabet. 1:01

The relationship between the two sets can be illustrated with an Euler diagram. 1:07

In an Euler diagram, one circle is completely enveloped by the other. 1:14

We can describe the relationship between the sets in two ways. 1:20

The vowel set is a subset of the alphabet set and 1:24

the alphabet set is a superset of the vowel set. 1:29

Sets can also have no members in common. 1:34

A set of digits would be represented by a separate circle. 1:37

In the two circles, alphabet and digits do not touch each other. 1:42

We say that they are disjoint sets. 1:48

Which letters are vowels? 1:54

This is a question of membership testing. 1:57

We can use the in keyword to find out. 2:00

Is A in vowels? 2:13

It's true. 2:16

How about B? 2:18

So A is in vowels, but B is not. 2:23

We can test the opposite by using the not in keywords. 2:27

Is C not in vowels? 2:42

It's true. 2:45

How about D? 2:47

So A is in vowels, B is not in vowels, and C and D are also not in vowels, and so on. 2:52

That's membership testing. 3:00

Now on to relations. 3:03

Every letter that is a vowel can be found in the letters of the alphabet. 3:05

Let's make a set of letters of the whole alphabet. 3:10

Instead of typing out all of the letters one by one, I'm going to import 3:14

the string module which has constants for situations just like this. 3:19

The constant that I want is called ascii_lowercase. 3:25

It's a string of lowercase letters, I can show you in the interpreter. 3:35

Since a string is an iterable, 3:51

I can use the set constructor function to make it a set. 3:53

Now I have a set of all of the letters in the alphabet. 4:05

Let's prove programmatically that all members of the vowel set are also 4:13

members of the alphabet set. 4:17

I can loop through every letter of vowels and perform a membership test. 4:23

Is that letter in the alphabet? 4:34

If it is, I'll have a flag and I can change it to true. 4:37

If it isn't, change the flag to false. 4:49

And it has to be true for every letter involved. 4:55

So if it's false just once, we can break the loop. 4:59

I'll turn my pseudocode into 5:05

some implementation code now. 5:10

And if my is_related flag is True, then I wanna print out 5:38

a nice message to let me know that these two sets are related. 5:42

Let's run the code and see what happens. 6:07

Something went wrong here. 6:18

So I think my loop logic is correct, so I'm gonna scroll up to continue debugging. 6:20

And, right here on line 3, I have capital letter vowels, 6:27

but on line 4, I'm using my lowercase constant, 6:33

when really I need to have ascii_uppercase. 6:38

Let's hop back into the terminal and 6:42

interpreter mode to see what that looks like. 6:46

A string of all uppercase letters, great. 6:55

Now let's run my script again. 6:59

So for every letter in the vowels, if the letter is in the alphabet, 7:03

we can change the is_related flag to true. 7:08

And if all of those letters are in the alphabet, 7:11

then we'll print out this message that the two sets are related. 7:14

It's related, yay! 7:18

We can say that the vowel set is a subset of the alphabet set. 7:22

I've proven it to you with a couple blocks of code, but 7:27

you can also check by calling the built-in set method issubset. 7:31

To demonstrate this method, I'm actually gonna open my script 7:36

in interpreter mode, python3 -i set_membership.py. 7:41

It's related, and I can check that 7:46

my vowels.issubset(alphabet). 7:52

When I return here, this should say true. 8:01

Each and every vowel is contained in the set of all of 8:06

the letters in the alphabet, it's true. 8:10

Inversely, we can say that the alphabet set is a superset of the vowel set. 8:13

It's True, out of all of the letters in the alphabet set, 8:27

we can also find the letters that are our vowels. 8:32

issubset and issuperset can also be performed with shorthand operators. 8:37

Shorthand means less typing. 8:42

Instead of issubset, we can use the less than or equal sign. 8:45

It's true, vowels is a subset of the alphabet. 8:57

And instead of issuperset, we can use the greater than or equal sign. 9:03

It's True, still True. 9:14

You can check out my teacher's notes for 9:17

a handy reference of the shorthand operators in the rest of this workshop. 9:19

Earlier, we used another comparison operator on sets, the double equal sign. 9:24

Two sets are equal to each other only if they have the exact same membership. 9:29

These three comparison operators will return true when 9:45

comparing a set with itself. 9:50

Let's make a set of digits using the string module. 9:52

First, I'll exit out of my interpreter and I'll come back to my script. 9:57

And I can get rid of this block right here since we're using a new example. 10:03

We'll say digits = string.digits. 10:11

And I can make this into a set. 10:17

Digits and alphabets are sets that have no members in common. 10:25

We can say that the two sets are disjointed, 10:30

digits.isdisjoint(alphabet). 10:34

We can print this. 10:41

It's True, there's no shorthand operator for disjoint, so 10:48

you'll just have to settle for using the method call instead. 10:52

In the next video, 10:56

we'll explore more about set relationships using Venn diagrams. 10:57

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