The Algebra Of Prepositions

The branch of mathematics which deals with the symbols representation, vectors, specified Set of number, etc. with complete description is known as Algebra. Now we will study about the Algebra of propositions. Propositional formulas refer to propositions, propositional expressions, sentential formula, or we can say it is not a formula but a mere formal expression. It will be clear by taking an example: 'o + m' this does not denote any value, whereas representing the term as the value.
 
A propositional statement comprises of atomic proposition which is made by the means of any one or more propositions, generally named as connectives. Here atomic propositions is been taken into course to represent the fact which is co-related with the logical mechanism consisting of sequential expression for the representation of the facts to the algebra of proposition. Various occurrences create various queries at different Period of time in the same atomic proposition.

The binary operations satisfy many identities. These several identities have separate specified name. There are three pairs of laws which are stated below:
Propositions 1: For variables A, B, C the laws are shown below:
Commutative laws:
A U B = B U A,
A ∩ B,
Associative laws:
(A U B) U C = A U (B U C),
(A ∩ B) ∩ C = A ∩ (B ∩ C),
 
Distributive laws:
AU (B ∩ C) = (A U B) ∩ (AU B),      
 
A ∩ (B ∩ C) = (A ∩ B) ∩ (A ∩ C),
 
Proposition 2: For any of the ‘A’ subset of the pervasive set ‘Q’ the identities laws are:
A U ∅ = A,
A ∩ ∅ = A,
Complement laws:
A U A^C = Q
A ∩ A^C = ∅.