TOPIC 2 : SETS

What is sets in mathematics?

Set, is a basic concept of mathematics. The concept of a set is inseparable from a concept of an element. Sets have (or contain) elements, elements belong to sets. Roughly speaking, the terms set, collection, conglameration, class, assembly,group pile, heap and such might have been interchangeable, except that some of them have acquired special meanings in mathematics.

For example, the items you wear: shoes, socks, hat, shirt, pants, and so on.

I'm sure you could come up with at least a hundred.

This is known as a set.

Formula for sets:

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

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

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

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 

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.

An example of sets:

Example 1: 

Kyesha was in math class with her friend Angie. She whispered to Angie that she had just bought a set of winter clothes. The outerwear collection includes a coat, a hat, a scarf, gloves, and boots. What is a set of winter clothes?

A set is a collection of objects that have something in common or follow a rule. The objects in the set are called its elements. Set notation uses curly braces, with elements separated by commas.

A = {coat, hat, scarf, gloves, boots} is set of outwear that kyesha wear for winter clothes.

Example 2:  What is the set of all even whole numbers between 0 and 10?

Solution:

= {2, 4, 6, 8}  Note that the use of the word between means that the range of numbers given is not inclusive. As a result, the numbers 0 and 10 are not listed as elements in this set.

 Example 3: 

What is the set of primary colors the picture given?

Red, blue and yellow. We can use set notation to list the set of all primary colors.

X = {red, blue, yellow}

Questions for sets:

1. If U = {1, 3, 5, 7, 9, 11, 13}, then which of the following are subsets of U. 

B = {2, 4} 

A = {0}

C = {1, 9, 5, 13}

D = {5, 11, 1} 

E = {13, 7, 9, 11, 5, 3, 1} 

F = {2, 3, 4, 5} 

2. Let A = {2, 3, 4, 5, 6, 7} B = {2, 4, 7, 8) C = {2, 4}. Fill in the blanks by ⊂ or ⊄ to make the resulting statements true. 

(a) B __ A 

(b) C __ A 

(c) B __ C 

(d) ∅ __ B 

(e) C __ C 

(f) C __ B