Topic 4: Sets & Exercise

SETS

What is a sets??

A set is a group or collection of objects, considered as an entity unto itself. Sets are usually symbolized by uppercase, italicize, boldface letters such as A, B, S or Z. Each object or number in a set is called a member of element of a set. Every set is unique. it is not necessary to list every object in the set. instead, the rule that the objects follow can given in the braces. Examples include the set of all computers in the world, the set of all apples on a tree and the set of all irrational numbers between 0 and 1.

When the element of a set can be listed, it is customary to enclose the list in curly brackets. thus for example we might speak of the set (call it K) of all natural numbers between and including 5 and 10 as:

k = {5, 6 7, 8, 9 }

Numerical Sets

So what does this have to do with mathematics? When we define a set, all we have to specify is a common characteristic. Who says we can't do so with numbers?

Set of even numbers: {..., -4, -2, 0, 2, 4, ...}
Set of odd numbers: {..., -3, -1, 1, 3, ...}
Set of prime numbers: {2, 3, 5, 7, 11, 13, 17, ...}
Positive multiples of 3 that are less than 10: {3, 6, 9}

And the list goes on. We can come up with all different types of sets.
There can also be sets of numbers that have no common property, they are just defined that way. 

For example:

{2, 3, 6, 828, 3839, 8827}
{4, 5, 6, 10, 21}
{2, 949, 48282, 42882959, 119484203}

Are all sets that I just randomly banged on my keyboard to produce.

Why are Sets Important?
Sets are the fundamental property of mathematics. Now as a word of warning, sets, by themselves, seem pretty pointless. But it's only when we apply sets in different situations do they become the powerful building block of mathematics that they are.

Math can get amazingly complicated quite fast. Graph Theory, Abstract Algebra, Real Analysis, Complex Analysis, Linear Algebra, Number Theory, and the list goes on. But there is one thing that all of these share in common: Sets.

Formula for sets:

1)   ◡  mean       ➡   "Union of sets" which mean "include the all number"


2)       ∩     mean      ➡    "Intersection of sets" which mean give "the same parts number"


3)      A'         mean       ➡   "Not A" which mean "include all the alphabet except for A"
 

Example 1:

 Question: What is the set of primary colors?

Solution:  There are red, blue and yellow. We can use set notation to list the set of all primary colors. Such as:

X = {Red, Blue, Yellow}

Let's try example 2 by using the the numeric.

Example 2:

Question: Let H be the set of all numbers less than ten

Solution: H {1, 2, 3, 4, 5, 6, 7, 8, 9}

Below is the example picture of sets by using the venn diagram:

Example 3: A {x : x Є N, x < 5}

A= {1, 2, 3, 4}

Therefore, n(A) =4

B = set of letters in the word ALGEBRA

B = {A, L, G, E, B, R}

therefore, n(B) = 6   

This is the video of sets that can teach you guys. Hopefully this video can make you fully understand in sets. Let's watch it!!!

 

EXERCISE

Let A = {a,b,e,f,h,i}    Let B= {a,c,e,g}     Let C= {d,g,i}

Find: 

1) A ∩ B




2) B ∩ C




3) A ∪ B ∪ C




4) B ∪ C

TRY YOUR BEST. YOU CAN DO THIS👍