8. Set Theory & Data Analysis
A collection of non-repeating (unique) elements is called a set.
e.g. The set of letters in "November" is {\$N,O,V,E,M,B,R\$}
A set X that is completely contained in another set Y is called a proper subset.
X is a "simple" subset of itself.

The set of common elements between two sets X and Y is called their intersection set
The set of all elements in X, in Y, and in their intersection, is called their set union
The set of all elements in X but not in Y is denoted by \$X-Y\$ and is called a set difference
Please note that X-Y may not equal Y-X. e.g. \$X\$={\$1,2,4,5\$}, \$Y\$=[\$2,3,5,6\$}. \$X-Y\$={\$1,4\$}, while \$Y-X\$={\$3,6\$}
The number of elements of a set is called its cardinality.
The set of all elements under consideration is called a sample space

We can draw sets and subsets in a sample space and draw interesting inferences about our data. This diagram is called a Venn Diagram

A Venn diagram makes relationships between sets clear. For example:
If 150 cars are registered today at a DMV of which 30 are Toyotas, and 30 are red, and 5 are both, then how many are neither?
Total sample space=150 cars, X(Red)=30, Y(Toyota)=30, intersection(X,Y)=5
So, Red non-Toyotas=\$30-5=25\$, Non-Red Toyotas=\$30-5=25\$.
Which leaves a total of \$150-(25+25+5)=95\$ cars that are non-red, non-Toyotas of the 150 cars registered today.