If and only if ($ \Leftrightarrow $) − $A \Leftrightarrow B$ is bi-conditional logical connective which is true when p and q are same, i.e. Implication / if-then ($\rightarrow$) − An implication $A \rightarrow B$ is the proposition “if A, then B”. Negation ($\lnot$) − The negation of a proposition A (written as $\lnot A$) is false when A is true and is true when A is false. OR ($\lor$) − The OR operation of two propositions A and B (written as $A \lor B$) is true if at least any of the propositional variable A or B is true.ĪND ($\land$) − The AND operation of two propositions A and B (written as $A \land B$) is true if both the propositional variable A and B is true. In propositional logic generally we use five connectives which are − It is because unless we give a specific value of A, we cannot say whether the statement is true or false. "12 + 9 = 3 – 2", it returns truth value “FALSE”."Man is Mortal", it returns truth value “TRUE”.Some examples of Propositions are given below − The connectives connect the propositional variables. We denote the propositional variables by capital letters (A, B, etc). A propositional consists of propositional variables and connectives. Prepositional Logic – DefinitionĪ proposition is a collection of declarative statements that has either a truth value "true” or a truth value "false". The purpose is to analyze these statements either individually or in a composite manner. Propositional Logic is concerned with statements to which the truth values, “true” and “false”, can be assigned. It has many practical applications in computer science like design of computing machines, artificial intelligence, definition of data structures for programming languages etc. Logical reasoning provides the theoretical base for many areas of mathematics and consequently computer science. Greek philosopher, Aristotle, was the pioneer of logical reasoning. The rules of mathematical logic specify methods of reasoning mathematical statements.