Abstract
This chapter describes the propositional calculus and its applications in mathematical proofs. Constructing proofs is a procedure that is characteristic of mathematics. Constructing proofs consists of obtaining certain theorems from other theorems whose validity has been established earlier or which have been accepted as initial theorems or axioms. Obtaining theorems from other theorems is based on what is called deductive reasoning, which is an instrument of mathematics. Mathematical logic is that discipline whose primary task is to study the nature of the reasonings used in mathematics and to establish criteria for their correctness. An elementary discussion of the two branches of mathematical logic—the propositional calculus and the functional calculus—with special reference to their applications in mathematical proofs are presented in the chapter. The chapter also discusses propositional connectives and the concepts of rules of inference and the rule of detachment.
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