Validity of an argument

There are two forms of reasoning used in mathematics namely, inductive reasoning and deductive reasoning.

Inductive reasoning usually lacks generality because not all possibilities have been exhausted, when we use inductive reasoning, we base our conclusions on observation or experiences.

On the other hand, deductive reasoning is the process of showing that certain statements are accepted as true.  In deductive reasoning all possibilities have been exhausted and therefore a generalized conclusion can be made.

Valid argument may be referred to a deductive arguments because deductive reasoning is based on conclusions reached from valid arguments.  In deductive reasoning, we start with assumptions (also called hypotheses or premises) and then draws a conclusion based on those assumptions.

An argument may be described as a set of statements or proposition called the premises which leads to a conclusion.  Let P₁, P₂, P₃ ………..P_n represent the premises of an argument and C represents the conclusion.  A valid argument is one in which if the premises P₁, P₂, P₃…… P_n are         all true, the conclusion C will always be true.  In other words, an argument is said to be valid if the conjunction of the compound statement i.e  P₁ ^ P₂ ^ P₃…… ^ P_n­  is tautology.  If an argument is not valid, it is called invalid or a fallacy.  This, argument is valid if the conclusion follows from the hypotheses.

WRAP UP AND ASSESSMENT

A Proposition is a statement that is either true (T) or False (F) but not both.

A compound statement or proposition is made up of two or more simple statements joined by the connectives.  Ex 10.1 No 1, 2