Introduction to Set Notation – P6

Hello.

My name is Daniel Cheetah.

I'm an associate professor at Durham University.

This is my second course on property.

In this mini lecture,

we look at the introduction to set theory.

Up until now,

we've been writing out our events in longhand.

We would like to do this in a much more compact notation.

Think, for example, sheet music for musicians or traffic signals on the road

in maths, we do this using set theory

for sets. We use curly brackets

and then inside the curly brackets, we have stuff inside the sense.

Let's have a look at some examples.

First example is we have a set of elements A, B and C.

So this is a set of three elements containing A, B and C.

The next set that we've got

is a set of numbers

from 13 to 6.

So we have open brackets.

123456 and then close brackets.

Mhm

now sets. We can have anything included in them,

for example, colours

so we could have a set of colours red, orange, yellow, green, blue and violet.

We use the notation e to represent an element of Oran.

So where you see this symbol Just think element of or in.

So for example, three e. D. Set one through to six.

Just means three is an element of 123456 or three is in 123456.

Here we have a e of ABC. So this means that a is in ABC.

Another notation that we use is

Sai

Sai is the universal set.

This is the set where all elements are considered.

Let's have a look at some more examples on sets

so we can look at the set of prime numbers under 30.

These are given by 2357, 11 13 17 1923

29.

Or the set of letters

in the word Masalit.

This is M A

S

O

L

I t

notice that we don't repeat the s. We just include at once an asset.

We can also combine sets.

There are two ways to do this.

One is intersections

and we write a upside down cup

B.

So what this means is a intersect B,

and this identifies the elements that are in a

and B

the other way that we can combine sets is we can take the union

so we write a

Cup B

so this means a union be

so this identifies the elements that are in a or B.

Let's have a look at some examples.

Let's suppose that we take a to be the set of numbers.

13479 and 10

and B two b The set of numbers 235 and nine.

Then we can find a union. Be

remembering that these are the elements that are in a or B.

So this is 1234579 and 10

because each of the elements in

this set here is either in a

or

the R and B.

Similarly, we can look at the elements are in a

Intersect. Be

remembering that these are the elements are in A and B.

There are only two here.

The number three is in both A and B,

and the number nine

is also in A and B.

We can also look at getting sets from tables.

So, for instance, let's suppose we have the following frequency table.

So we have one person that owns a cat and a dog.

We have two people that owns a cat and no dog.

We have four people that own

no cat but own a dog.

And we have three people

that own no cat

and they own no dog.

So we'll label d. I s to be the person that owns a dog and no cat

see eye to be the person that owns a cat and no dog.

The B I is to be people that own both a dog and a cat

and then I to be people that do not own a cat or a dog.

Now we can record

these people,

so we've got to be one person because

this is a person that owns both a cat and a dog.

We've got two people that just only cut and no dogs. So we've got C one and C two.

Then we've got four people that own dogs and the cats. So we've got the one up to D four

and then we got three people that own

no dog and no cap. So we've got n one up to N. Three

here. The subscript is just used as labelling to identify different people