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Algebra of Logic |
Algebra of Logic
Algebra of Logic or Boolean algebra is a branch of mathematics. It deals with variables and their truth value. The variables have two possible states – true
or false
.
It was first introduced by George Boole in his book The Mathematical Analysis of Logic (1847).
Boolean algebra is fundamental to the development of digital electronics. It is responsible for making possible all modern computing.
The three basic operations in Boolean Algebra are AND
, OR
, and NOT
. Consider two boolean variables x
and y
:
x AND y
is true if and only if bothx
andy
are truex OR y
is true if and only if either ofx
,y
are true. Ifx
,y
are both true,x OR y
is still trueNOT x
is true if and only ifx
is false and vice versa
NOT
of boolean statements can be refactored to apply directly to each variable. Consider the following :
NOT (x AND y) = NOT x OR NOT y
NOT (x OR y) = NOT x AND NOT y
The above statements are called "De Morgan's Laws." This is a very useful and important law in Boolean Algebra.
More Information:
- The Calculus of Logic: George Boole
- Boolean algebra article: Wikipedia
- Boolean Algebra Demonstration: Boolean Algebra