Propositional Logic

Logic is a formal method of reasoning. Logic can be symbolically represented in many ways such as propositional logic, digital logic, Boolean algebra etc. One such way of doing so is propositional logic. The propositional logic represents logic through propositions and logical connectives. Proposition is an elementary atomic sentence that may either be true or false. Propositions are of two type’s simple propositions and compound propositions. Simple proposition does not contain any other proposition as a part. It uses lower case letters. Compound proposition is the one with two or more simple propositions as parts. It is a part of simple proposition.

Operator is used to join the simple proposition to make the compound proposition. Different symbols are used to designate the sentential connectives. The different types of connectives or operators are disjunctive, conjunctive, conditional, bi-conditional, negation. Disjunctive connective is also known as OR and is represented by disjunction symbol. Conjunctive is also known as AND. It is represented by the conjunction symbol. Conditional connective is also known as ‘If - then’ or implication. Implication means if one argument is true then the other argument is true. Bi-Conditional is also known as if and only if or equivalence. Equivalence means either both are true or both are false. Negation is also called as NOT or unary operator. It is an operator that affects a single statement only and does not join two or more statements. Proposition that is always true is known as tautology. Contrapositive is conditional statement whose antecedent is the negation of the original consequent and whose consequent is the negation of the original antecedent.

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