SET THEORY

SET THEORY

A set is a well-defined as the COLLECTION or GROUP of an object,things or numbers.

For instance;

Consider the application you have on your phone.

Gmail

Contacts

Google Play store

YouTube

Facebook

Clock

e.t c

This is a collection of your phone app and can be regarded as a SET

Note: The SET must have a name to defined and differentiate it from other SETS.

Hence the name of this SET can be MYPHONEAPP

And the members in the SET ; MYPHONEAPP are Gmail, Playstore,Contacts e t.c

Just think of any collection

Materials in make up kit✅

First aid box tools✅

Subjects offered by a student✅

States in Nigeria✅

A-ELITE ACADEMY Students✅

And lot more........

Note: It can be a number as well and this is what we'll mostly work it as mathematics deals with the science of numbers

 Even numbers from 0 to 10✅

Factors of 3 less than 60✅

Prime numbers less than 15✅

e.t.c

Z= {-3,-2,-1,0,1,2,3}

Note: The SET NAME is usually denoted by CAPITAL LETTER such as (Z) While the elements of a set are denoted by small letter such as a,b,c,d,e.........

In a nut shell, we can as well have 

A= {a,b,c,d,e}

 SETs are usually enclosed by Curly brackets as {}

 Now SET can either  be given in intrinsic format or extrinsic format.

A= {All prime number between 1 and 10}. INTRINSIC

A= {2,3,5,7}

A= {All prime number between 1 and 10}. INTRINSIC

A= {2,3,5,7}. EXTRINSIC

 Can you now see the difference between the INTRINSIC and EXTRINSIC Format✍🏾

The set can be gven to you by the examiner in whichever way

All you need to do is to have the basic knowledge as to how to convert it mostly to a workable format which is the EXTRINSIC

Each item in a SET is known as member or ELEMENT

 So if a set is defined as Students of A-ELITE ACADEMY;

Then you're an element of that set since you're a student of A-ELITE ACADEMY

 But now let's see if Joe Biden is an element of that set.

No! Because Joe Biden is not a student of A-ELITE ACADEMY

Symbols and their interpretation

 Student of A-ELITE ACADEMY= {Samuel,Taiwo,Ola,Kemi, Martins,David}

Samuel is an element of the SET but Promise is not

CLASS EXERCISE:

 Interpret all of this in EXTRINSIC FORMAT 

1. P = Set of odd numbers less than 20

2. Q = Set of Even numbers less than 20

3. R= Set of Prime numbers less than 20

4. S = { -3 < x < 5}