![]() ![]() both are false or both are true.Ī Tautology is a formula which is always true for every value of its propositional variables.Įxample − Prove $\lbrack (A \rightarrow B) \land A \rbrack \rightarrow B$ is a tautologyĪs we can see every value of $\lbrack (A \rightarrow B) \land A \rbrack \rightarrow B$ is "True", it is a tautology. 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.
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