Transcript SET THEORY and VENN DIAGRAMS

T Bolan
SET THEORY
and
VENN DIAGRAMS
Words used to describe
Automobiles
4-wheelers
Cars
gas
2-door
2-wheelers
Ford
Trucks
18-wheelers
new
Mitsubishi
Farrari
Old
blue
Solar
4-door
green
red
vans
diesel
3-wheelers
Motorcycles
We can use these words to
categorize cars into types
4-wheelers
Cars
gas
2-door
2-wheelers
Ford
Trucks
18-wheelers
new
Mitsubishi
Farrari
Old
blue
Solar
4-door
green
red
vans
diesel
3-wheelers
Motorcycles
Now, pretend for a second that this box, represents
“Crazy Bob’s Autos” parking lot.
Every car in existence
motorcycles
18-wheelers
And everyone sold
their car to
Crazy Bob
So he has every
car in existence,
1. Where do I go to
find a motorcycle?
Where do I
Find an 18-wheeler?
3. Where do I get a
Blue car?
Where would I look
to find a blue car if I
don’t want an
18-wheeler?
Where would I look
to find a blue car if I
don’t want an
18-wheeler or a
motorcycle?
What about if I want
a motorcycle but not
a blue one?
What If I don’t care
what I buy, as long
as it isn’t blue?
These are pretty easy
it actually takes longer
to read the question
than it does to answer
it.
Let’s simplify this
The symbol
 means INTERSECTION
It means both.
If you want a blue motorcycle,
BM
Then you want blue and motorcycle
The symbol
 means UNION
It means either.
If you want any Motorcycle OR
Anything Blue
BM
What does this look like?
BE
What does this look like?
BE
What does this look like?
M E
What does this look like?
M E
They don’t overlap.
When there is no answer,
There is no such thing
We call it the
EMPTY SET
Here we are asked for a
Motorcycle that is also an 18-wheeler
Or NULL SET
Before we go any further, let’s make sure we understand the
NULL SET.
It is not the same as zero.
How many donkeys have walked on the moon?
0
How many donkeys should you eat to turn your hair purple?
NULL SET
Zero donkeys is not the right answer.
This question has no answer.
Something is wrong with the question.
“I want a motorcycle or an 18-wheeler”
M E
“Anything but motorcycle or
an 18-wheeler”
If we draw a bar above it.
It means the opposite.
M E
“I want an 18-wheeler”
E
“Anything but an 18-wheeler”
E
“I want a blue motorcycle”
M B
“Anything but a blue motorcycle”
M B
B
“I don’t care what I get, as long as it isn’t blue”
In the box is every student in the school.
M for kids in your MATH class
S for kids in your SCIENCE class
G for kids in your GYM class
Students in Math OR Science
M S
Students in Math AND
Science AND Gym
Students in Math AND Science
M S
Students NOT in Gym or Math
M  S G
M G
Students NOT in Gym or Math
M G
Students NOT in Gym AND Math
M G
In other words: you start to tell a
joke in math class, but the bell rings
And you have to finish it in gym.
These guys heard the whole joke
Sooo everyone else
Who DOESN’T get the joke?
M S
M S
M S
M S
M S
M S