INTRODUCTION
1. In 1854, George Boole has introduced a systematic
treatment of logic which is known as ‘Boolean Algebra’.
2. In Boolean Algebra 1+1=1 whereas in
binary number system 1+1=10.
3. The Boolean Algebra is defined with a
set of elements set of operations and number of rules, laws, theorems and
postulates.
4. The posulates is a mathematical
systems from which we can deduce laws, rules and theorems.
+ and . (dot)
AXIOMS OF BOOLEAN ALGEBRA
A. Closure
with respect to the operator ‘+’ i.e. when the vinary elements are operated by + the result is unique binary element.
B. Closure
with respect to operator ‘∙’ i.e. when the binary elements are operated
by ‘ ∙’ operator then the result is
unique binary element.
C. An
identity element with respect to ‘+’
desiginated by 0.
Example:- A+0=A
0+A=A.
D. An
identity element with respect to ‘∙’
desiginated by 1.
Example:- A*1=A
1*A=A.
E. Commutative
withrespect to ‘+’ i.e. A+B=B+A.
F. Commutative
with respect to ‘∙’ i.e. AB=BA.
G. Distributed
property of ‘∙’ over ‘+’ is A∙(B+C)=(A∙B)+(A∙C).
H. Distributed
property of ‘+’ over ‘∙’ is A+(B∙C)=(A+B)∙(A+C).
I. For every binary element there exists a
complement i.e.
if A=0, then A`=1
if A=1, then A`=0.