The section of abstract mathematics concerning two values: true and false.
June 23, 2017—Patrick Griffin
History
George Boole introduced Boolean algebra in 1847 as part of his book, The Mathematical Analysis of Logic. The approach was then fine-tuned by William Stanley Jevons and Ernst Schröder in the late 19th century. The system was applied to circuitry in the 1930s when Claude Shannon, a mathematician and electronics engineer, made the realization that Boolean algebra could be used as tool to analyze logic gates. Any system using sentential logic will also have a way of representation in Boolean algebra.
Rules of Boolean Algebra
There are 13 basic laws of Boolean algebra.
In[]:=
Rules
"A+1=1"
"A+0=A"
"A*1=A"
"A*0=0"
"A+A=A"
"A*A=A"
"-(-A)=A"
"A+-A=1"
"A*-A=0"
"A+B=B+A"
"A*B=B*A"
"-(A+B)=-A+-B"
"-(A*B)=-A*-B"
These concepts can be easily be represented using Mathematica’s built-in functions.
Rule 1:
A||1==1
:
In[]:=
True||1//Boole
Out[]=
1
Shouldn’t this rule be input as follows (parentheses are required because of operator precedence)?