Basic Properties Of Boolean Algebra
Tuesday, January 11, 2011
A Set of element in the Boolean System indicated by {B=a, b, c,…} has two binary operation AND (.), OR (+) and one unary operator NOT (´). The basic properties of the system are:
1.Both the operations are commutative,
* a+b=b+a
* a.b=b.a
2.Identity elements are there in both the operations,
* a+0=a
* a.1=a
3.Each operation is distributive with respect to the other.
* a+(b.c)=(a+b).(a+c)
* a.(b+c)=(a.b)+(a.c)
4.There exists a´ for each a∈b such that
* a+a´=1
* a.a´=0
Example: Given the set {0,1} of two elements, where the elements have been denoted by the symbols 0 and 1 as is customary and they have no relation with the numbers 0 and 1 used in arithmetic. Let the two binary operations be denoted by + known as logical addition and (.) known as logical multiplication which have no relation to the operations of addition and multiplication used in arithmetic. In tables 1 and 2 are given the logical sum and logical products, i.e., the results of the above operations on the elements of the set.
Solution: Both the operations are Boolean because of the following properties….
In view of these properties of the set {0, 1} and the definition of (+) and (.) as given by the tables 1 and 2, we conclude that it is Boolean Read more...
