Set notation
There is special notation
that is used to describe interactions of sets. This notation is made of combinations of four symbols:
This is a union
symbol. You write it between two
sets names in the same way you write a + or – between two numbers. It means take all of both sets. If my sets are A: people who like
apples, and B: people who like bananas, all of these mean the same thing:


People who like apples
or bananas. (notice that "or" goes between the two attributes or conditions that define the set) 
Union means putting together.
The United States is the union of the 50 states
This is an intersection symbol. You write it between two sets
names in the same way you write a + or – between two numbers. It means to take the overlap of the two
sets. If my sets are A: people who like apples, and B: people who like bananas,
all of these mean the same thing:


People who like apples
and bananas

Intersection means an overlap
or a meeting. When you drive
through an intersection, the intersection is the overlap of the two streets.
This is a
complement symbol. You write it
over the top of the name of a set.
It means to take everything that is not in that set. If my sets are A:
people who like apples, (and B: people who like bananas,) all of these mean the
same thing:

or 
People who don’t
like apples 
Complement means something
like opposite: red and green are complementary colors. They are different, and between them they
use the 3 primary colors (red, yellow, blue). (Note the spelling difference between complement and compliment)
Both of these
symbols can represent set subtraction.
We will use – in this class. You write it between two sets names
in the same way you write a + or – between two numbers. It means to take
everything that is in the first set, but not in the second set. You don’t
ever have to use set subtraction, because you can do the same thing by
combining intersections and complements, but it makes some things a lot
simpler. If my sets are A: people who like apples, (and B: people who like
bananas,) all of these mean the same thing:
AB or 

People who like apples
but not bananas. 
Set subtraction is a lot like
number subtraction in that it is a takeaway concept, but it looks funny
because the second set is not always a subset of the first set. You can’t just look at the number
of elements in the sets in order to do a set subtraction, you actually have to
look at the elements in the sets