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The Algebra of Prepositions

Sub Topics

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 AC = Q
A ∩ AC = ∅.

Logical Arguments

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The term 'Logical Argument' is made with two words logic and arguments first we will understand its meaning. Logic deals with the study of evaluation of argument and reasoning. Logic enables us to reason correctly it helps to get the difference between what is correct and what is inaccurate. The term logic arguments help us to reach to the final result of a particular thing on which discussions are taking place. Moreover it helps to get the true and fair side of the argument making a complete sense and reliability with a fledged reasoning. By understanding few terms we will easily be able to get the answers of our logical arguments.
Some properties of arguments:
Ascertainment of arguments- It is necessary because of its ascertainment the argument will not work out, because there is a difference between the argument and mere statement, although it is not a easy job to make the difference because arguments are also conducted in an ordinary language, but there is no need to worry about that with a loud expression and Set of sentences form the argument. This is the way to separate the term argument or sentence. There are two inferences which will help us perfectly to differentiate between the argument and propositions. The first inference is deductive inference which states a simple meaning that when in the conclusion of the matter the truth has the firm guarantee, then it will be considered as deductive inference. It holds the correctness and reliability at high standards. The other inference is Inductive inference which holds the truth likely or with the less Probability of correctness but it needs some evidences or proof on the grounds of truth and reliability.
On the grounds of differentiation we can easily examine the truth or reach to the conclusion of logical arguments.