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The concept of membership is
a distinguishing feature of sets.

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Recall that an element of
a set is called a member.

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The concept of membership
testing means asking whether or

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not an element is a member of a set.

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

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

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

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Is it there or not?

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Membership testing can
be performed on one set.

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

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determine how different sets
are related to each other.

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For example,
what happens when all of the members of

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one set are also members of another set?

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

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also members of the set of
letters of the English alphabet.

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

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

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We can describe the relationship
between the sets in two ways.

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The vowel set is a subset
of the alphabet set and

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the alphabet set is
a superset of the vowel set.

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Sets can also have no members in common.

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

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

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We say that they are disjoint sets.

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Which letters are vowels?

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This is a question of membership testing.

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We can use the in keyword to find out.

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Is A in vowels?

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It's true.

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How about B?

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So A is in vowels, but B is not.

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We can test the opposite by
using the not in keywords.

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Is C not in vowels?

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It's true.

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How about D?

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

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That's membership testing.

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Now on to relations.

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

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

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

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

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The constant that I want
is called ascii_lowercase.

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

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Since a string is an iterable,

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

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

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

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members of the alphabet set.

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

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Is that letter in the alphabet?

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

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

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And it has to be true for
every letter involved.

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

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I'll turn my pseudocode into

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some implementation code now.

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

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

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Let's run the code and see what happens.

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Something went wrong here.

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

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

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

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when really I need to
have ascii_uppercase.

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Let's hop back into the terminal and

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interpreter mode to see
what that looks like.

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A string of all uppercase letters, great.

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Now let's run my script again.

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So for every letter in the vowels,
if the letter is in the alphabet,

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we can change the is_related flag to true.

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And if all of those letters
are in the alphabet,

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

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It's related, yay!

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

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

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

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

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in interpreter mode,
python3 -i set_membership.py.

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It's related, and I can check that

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my vowels.issubset(alphabet).

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When I return here, this should say true.

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Each and every vowel is
contained in the set of all of

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the letters in the alphabet, it's true.

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

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

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we can also find the letters
that are our vowels.

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issubset and issuperset can also be
performed with shorthand operators.

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Shorthand means less typing.

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

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

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

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It's True, still True.

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You can check out my teacher's notes for

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

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

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

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These three comparison
operators will return true when

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comparing a set with itself.

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

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

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

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We'll say digits = string.digits.

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And I can make this into a set.

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

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We can say that the two
sets are disjointed,

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digits.isdisjoint(alphabet).

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We can print this.

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

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

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In the next video,

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