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# Pre-cal Logic

### Flash Cards for Mrs. Wag's Logic Chapter

Question | Answer |
---|---|

Mathematical Logic | symbolic, Bertrand Russel & A. N. Whitehead (England Principia Mathematica) |

Statement | a sentence that states a fact or contains a complete idea. Can be judged T or F. |

Negation | ~ results in opposite truth values |

Quantifiers | some, all, one, none |

~ Some | “for some p” > “for all not p” |

~ All | “for all p” > “for some not p” |

Conjunction | p^q. 2 statements connected by “and” |

Disjunction | pvq. 2 statements connected by “or” |

Conditional/Implication | p > q. |

Converse | q > p. |

Biconditional | whenever both the conditional and converse are T, p and q have = T values. |

Tautology | compound statement that is always T regardless of the T values of its components. the biconditional of 2 = statements. |

Logically Equivalent | 2 statements that have the same T values. |

Inverse | ~p > ~q |

Contrapositive | ~q > ~p |

Law of Detachment (def) | if a conditional is T and its hypothesis is T, then its conclusion must be T |

Law of Modus Tollens (def) | if a conditional is T and its conclusion is F, then its hypothesis is F |

Law of Contrapositive (def) | if a conditional is T then its contrapositive is T |

Law of Syllogism (def) | if 2 given conditionals are T a 3rd using the hypothesis of the 1st and the conclusion of the 2nd is T |

Law of Disjunctive Inference (def) | if a disjunction is T and one of the disjuncts is F, then the other disjunct is T |

Law of Disjunctive Addition (def) | if a given statement is T then a disjunction involving that statement and any 2nd statement is T |

Law of Simplification (def) | if a conjunction is T then each of the conjuncts is T |

Law of Conjunction (def) | if two statements are T, the conjunction is T |

Negation of Conjunction (def) | the negation of a conjunction = the disjunction of the negation of each statement |

Negation of Disjunction (def) | the negation of a disjunction of two statements = the conjunction of the negation of each statement |

Law of Double Negation (def) | the negation of the negation statement is = to the statement |

Invalid Reasoning (Asserting the Conclusion) | if a conditional is T and its conclusion is T then its hypothesis is not necessarily T |

Invalid Reasoning (Denying the Premise) | if a conditional is T and its hypothesis is false then its conclusion is not necessarily F. |

Law of Contrapositive (argument) | |

Law of Detachment (argument) | |

Law of Modus Tollens (argument) | |

Law of Syllogism (argument) | |

Law of Disjunctive Inference (argument) | |

Law of Disjunctive Addition (argument) | |

Law of Simplification (argument) | |

Law of Conjunction (argument) | |

Law of Double Negation (argument) | |

Negation of a Conjunction (argument) | |

Negation of a Disjunction (argument) | |

Invalid Reasoning, Asserting the Conclusion (argument) | |

Invalid Reasoning, Denying the Premise (argument) |

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YellowDucks