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Encyclopedia > Biconditional introduction

Biconditional introduction is the inference that, if B follows from A, and A follows from B, then A if and only if B.


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.


Formally:

 ( A → B ) ( B → A )  ∴ ( A ↔ B ) 

  Results from FactBites:
 
Maggie Johnson (934 words)
Biconditional Proof: Same as a conditional proof but it must be proven in two ways: A®B and B®A.
Conditional Introduction:  This is the formal counterpart of a conditional proof.
Biconditional Elimination: You can conclude Q if you establish P and either P « Q or Q « P. Biconditional Introduction:  To introduce P « Q, you must give two subproofs, one showing that Q follows from P, and one showing that P follows from Q. Prove: P ® Q «  (~Q ® ~P) Notes
  More results at FactBites »


 
 

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