Set notation page 3
Here are the complicated ones. (They're too hard for me to put on a test, but they are good exercise for your brain: if you can do these, you can do anything!)
All of the following say the same thing:
|
or
|
|
People who like apples
or bananas, but not both. or People who like apples
but not bananas, or* people who like bananas but not apples |
This one is really complicated.
The sentences on the right match the symbols on the left.
Order of operations says that you do
and
before -, so the first set of
symbols means take the union of A and B:
and then take away the intersection:
And what’s left is your
set:
In the second set of symbols,
I needed to use parentheses to get the order right. It says, do A-B:
and do B-A:
And take the union of those
two to get:
|
|
|
People who like both or
neither apples and bananas |
This one puts together the
one we just did, and the intersection.
|
or
|
|
People who don’t
like both apples and bananas or People who don’t
like apples or don’t like bananas. |
This is a lot like the first one on this page.
The first notation: 
says
first figure out the intersection:
and then take the complement
of that
The second notation: 
says
first figure out the complements:
And then take the union (keep
everything that is shaded in either version)
Here we are! the last funny,
complicated thing you can do with only two sets:
|
|
|
People who like bananas
or don’t like apples |
|
|
|
People who like apples
or don’t like bananas |
There are other ways of writing
correct set notation for these two, but I think these are the easiest.
For example, the first one says 
, take
the union of the sets A and the complement of B:
