By the end of the subtopic learners should be able to: 


M = {odd numbers between 0 and 12}
M = {1;3;5;7; 9;11}
X = {colors of the rainbow}
X = {red; orange; yellow; green; blue; indigo; violet}
V = {vowels}
V = {a; e; i; o; u}
N.B. Members of the set are contained is special brackets called set braces as shown in the given examples.
Notation  whAT IT REPRESENTS  WHat it means 

∅ or {}  Null set or empty set  A set with no elements 
ε  Universal set  A set which consists of all elements 
A∪B  Union of two sets  All elements in A and B collectively 
A∩B  Intersection of two sets  Common elements in both A and B 
n(A)  Number of elements in a set  Number of elements in set A 
∈  “…is an element of…”  $\mathrm{x}\in \mathrm{A}\to \mathrm{x}\mathrm{is}\mathrm{in}\mathrm{the}\mathrm{set}\mathrm{A}$ 
∉  “…is not an element of…”  $\mathrm{x}\notin \mathrm{A}\to $x is not in the set A 
A’  Complement of set A  All the other elements in the universal set that are not in the set A 
$\mathrm{A}\subseteq \mathrm{B}$  Subset  A is a subset of B 
$\mathrm{A}\subset \mathrm{B}$  Proper subset  A is a proper subset of B 
$\mathrm{A}\overline{)\subset}\mathrm{B}$  Not a proper subset  A is not a proper subset of B 
A=B  Equal sets  A and B have exactly the same elements 
S = {5; 10; 15; 20; 25; 30; 35}
n(S) = 7
P= {Monday; Tuesday; Wednesday; Thursday; Friday; Saturday; Sunday}
n(P) = 7
T = {January; February; March; April; May; June; July; August; September; October; November; December}
n(T) = 12
n(A) = 0
$\mathrm{B}=\left\{\right\}/\varnothing $
n(B) = 0
X = {10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20}
Y = {11; 13; 15; 17; 19}
All the elements of Y are contained in X therefore Y is a subset of X.
Two sets are equal when they contain exactly the same members or elements, even if they may not be in the same order.
Set A is equal to set B. This is represented as: A = B.
Two sets are equivalent if they contain the same number of elements.
P = {10;20;30;40;50;60}
S = {11;22;33;44;55;66}
Set P is equivalent to set S.
Union ($\mathrm{\upsilon}$)
In the diagram the region painted red represents the intersection of the two sets whilst the regions painted red, blue and purple put together represent the union of the two sets.
Given that F = {1; 2; 3; 4; 5} and G = {1; 3; 5; 7; 8; 9}, write down:
$\mathrm{P}\cap \mathrm{L}=\mathrm{X}$
Now that we have the value of x we are now able to fill in the actual numbers of elements in the regions of the Venn diagram.(Note that, 8 + 6 + 4 + 12 = 30, the total number of people in the meeting)
60 – x = 40
x = 20