Current state
Proof F low
Examples of Boolean Algebras
0-1 ( two valued )
Boolean algebra
OR / AND
Arithmetic Boolean
algebras (Boolean integers)
lcm / gcd
Algebra of subsets
union / intersection
Boole’s Original Motivation
Two- valued Boolean Algebra
 |
|
0 iff both x and y are 0 |
1 iff both x and y are 1 |
Is a Boolean algebra
Non-Binary Boolean Algebras
Elements:
The set of divisors of a Boolean integer
{1,2,3,5,6,10,15,30}
The operations : lcm and gcd
The special elements: 1 and 30
Algebra of Subsets
A set is a collection of points in a domain
Universal set: S is the set of all points
For example: S is the set of all books |
 |
Subsets:
A = red books
B = blue books
C = green books
D = German books
E = English books
F = French books
G = good books |
 |
| |
Venn Diagram
John Venn
1834 - 1923
 |
Euler Diagram
Leonhard Euler
1707-1783
|
|
