set theory and venn diagrams t bolan. words used to describe automobiles cars motorcycles trucks...

SET THEORY and

VENN DIAGRAMS

T Bolan

Words used to describe Automobiles

Cars

Motorcycles

Trucks

4-wheelers

2-wheelers

18-wheelers

3-wheelers

Ford

Mitsubishi Farrari

2-door

4-door

vans Old

new

gas

diesel Solar

green red

blue

We can use these words to categorize cars into types

Cars

Motorcycles

Trucks

4-wheelers

2-wheelers

18-wheelers

3-wheelers

Ford

Mitsubishi Farrari

2-door

4-door

vans Old

new

gas

diesel Solar

green red

blue

Now, pretend for a second that this box, represents “Crazy Bob’s Autos” parking lot.

And everyone sold their car to Crazy Bob

So he has every car in existence,

Every car in existence

motorcycles 18-wheelers

Blue cars

1. Where do I go to find a motorcycle?

Where do I Find an 18-wheeler?

3. Where do I get aBlue car?

Where would I lookto find a blue car if I don’t want an 18-wheeler?

Where would I lookto find a blue car if I don’t want an 18-wheeler or a motorcycle?

What about if I wanta motorcycle but not a blue one?

What If I don’t care what I buy, as longas it isn’t blue?

These are pretty easy

it actually takes longer to read the questionthan it does to answerit.

Let’s simplify this

The symbol means INTERSECTION

It means both.

If you want a blue motorcycle,

Then you want blue and motorcycle

MB

The symbol means UNION

It means either.

If you want any Motorcycle ORAnything Blue

MB

What does this look like?

EB

What does this look like?

EB

What does this look like?

EM

What does this look like?

EM They don’t overlap.

There is no such thing

Here we are asked for a Motorcycle that is also an 18-wheeler

When there is no answer,We call it the EMPTY SET

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?

Zero donkeys is not the right answer.

This question has no answer. Something is wrong with the question.

NULL SET

If we draw a bar above it. It means the opposite.

EM

EM

“I want a motorcycle or an 18-wheeler”

“Anything but motorcycle or an 18-wheeler”

E

E

“I want an 18-wheeler”

“Anything but an 18-wheeler”

BM

BM

“I want a blue motorcycle”

“Anything but a blue motorcycle”

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 Students in Math AND Science

Students in Math AND Science AND Gym

Students NOT in Gym or Math

SM SM

GSM GM

Students NOT in Gym or Math Students NOT in Gym AND Math

GM

In other words: you start to tell a joke in math class, but the bell ringsAnd you have to finish it in gym.

Who DOESN’T get the joke?These guys heard the whole joke

Sooo everyone else

GM

SM SM SM

SM SMSM