Biconditional introduction: Difference between revisions

Revision as of 21:54, 6 March 2012

Revision as of 20:24, 10 March 2012

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{{Transformation rules}}

In [[propositional calculus|propositional logic]], '''biconditional introduction''' is a [[validity|valid]] [[rule of inference]]. It allows for one to [[inference|infer]] a [[Logical biconditional|biconditional]] from two [[Material conditional|conditional statements]]. The rule makes it possible to introduce a [[logicalbiconditional biconditional|biconditional]]statement into a [[formal proof|logical proof]]. If <math>P \to Q</math> is true, and <math>Q \to P</math> then one may infer that <math>P \leftrightarrow Q</math> is true. For example, from the statements "if I'm breathing, then I'm alive" and "if I'm alive, then I'm breathing", it can be inferred that "I'm breathing [[if and only if]] I'm alive". Biconditional introduction is the [[Converse (logic)|converse]] of [[biconditional elimination]]. The rule can be stated formally as:

:<math>\frac{P \to Q, Q \to P}{\therefore P \leftrightarrow Q}</math>