Biconditional introduction: Difference between revisions

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Revision as of 12:33, 18 November 2006

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In [[mathematical logic]], '''biconditional introduction''' is the [[rule of inference]] that, if B follows from A, and A follows from B, then A [[if and only if]] B.

{{Wikify|September 2006}}

'''BiconditionalFor introduction'''example, isfrom the inferencestatements that"if I'm breathing, then I'm alive" and "if BI'm followsalive, fromthen AI'm breathing", andit Acan followsbe frominferred B,that then"I'm Abreathing [[if and only if]] BI'm alive".

Formally, biconditional introduction is the rule schema

For example: if I'm breathing, then I'm alive; also, if I'm alive, then I'm breathing. Therefore, I'm breathing if and only if I'm alive.

:<math> A \to B \, </math>

:<math> \underline{B \to A} </math>

Formally:

:<math> A \leftrightarrow B </math>

( A → B )

<u>( B → A )&nbsp;&nbsp;</u>

∴ ( A ↔ B )

[[Category:Logic]]