Given: A

¬A

Prove: B

Step | Justification |
---|---|

A ∧ ¬A | Assumed |

(A ∧ ¬A) ∨ B | The first clause is true, therefore the first clause or the second clause is true. |

¬¬((A ∧ ¬A) ∨ B) | A double negative is an affirmation |

¬(¬(A ∧ ¬A) ∧ ¬B) | DeMorgan's Laws |

¬((¬A ∨ A) ∧ ¬B) | DeMorgan's Laws |

¬((TRUE) ∧ ¬B) | Law of the Excluded Middle |

¬(¬B) | The truth of the conjunction is equivalent to the second clause. |

B | A double negative is an affirmation |

Any line of argument is susceptible to error. More confidence may be placed in a conclusion supported by multiple lines of argument.

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