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 }

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

Question

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

Find: 

1) A ∩ B




2) B ∩ C




3) A ∪ B ∪ C




4) B ∪ C