Introduction
Mathematical treatments of logic was presented in the middle of the nineteenth century,by, George Boole and then Augustus De Morgan.
Boole approached logic in a new way reducing it to a simple algebra, incorporating logic into mathematics.
George Boole 

In mathematical language, there are two kinds of reasoning  inductive and deductive. We are familiar with inductive reasoning as done in the chapter “Mathematical Induction”. Induction is a process of generalizing a concept from particular cases. Deductive reasoning on the other hand is using particular examples from a general situation. We shall discuss some fundamentals of deductive reasoning.