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# Logic

### Laws of Logic

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

MODUS PONENS (MP) -- direct reasoning applies to conditionals | If it rains, we will go to the movies. It rains. THEREFORE, we go to the movies. P-->Q and P, then Q |

MODUS TOLLENS (MT) indirect reasoning applies to conditional) | If it rains, we will go to the movies. We don't go to the movies. THEREFORE, it didn't rain. P-->Q and ~Q, then ~P. (works because of the logical equivalence of the contrapositive) |

LAW OF SYLLOGISM, a.k.a. "transitive property of conditionals" | P-->Q and Q-->R, then P-->R |

Simplification - applies to AND statements only (CONJUNCTIONS) | If you know P˄Q, then you can say P by itself or Q by itself, they're both true!! |

Equivalent Disjunctive (ED) -- magically turns a conditional statement into a disjunction OR | P --> Q ≡ ~P V Q |

Disjunctive Syllogism - applies only to a DISJUNCTION | Either we go to the movies, or we go bowling. We don't go to the movies. Then we must have gone bowling! PVQ and ~P, then Q |

Law of Contrapositive | P --> Q ≡ ~Q --> ~P |

The inverse and the converse of a conditional statement are logically equivalent | Because they're contrapositives of each other! Inverse: ~P --> ~Q Converse: Q --> P |

When is a disjunction false? Only one instance... | F V F = F |

When is a conjunction true? Only one instance.... | T ˄ T = T |

When is a conditional false? Only one instance, the broken promise... | T --> F = F |

To negate a conditional, first rewrite it as a disjunction using th equivalent dusjunctive... | Then use Demorgan's Law: ~P--> Q) ≡ ~(~P V Q) ≡ P˄~Q |

Other ways to say P --> Q "If P, then Q" | 1. P implies Q 2. Q if P 3. P only if Q |

When is the biconditional true? Only two instances... | When the two statements are the SAME truth value, i.e. T <--> T, F <--> F |

To translate the biconditional P <--> Q into words | P if and only if Q |

DEMORGAN'S LAW - negates conjunctions and disjunctions | ~(PVQ)≡ ~P ˄ ~Q ~(P˄Q)≡ ~P V ~Q |

The associative property only applies when all the conjunction/disjunction symbols are the same. Reassociate the parentheses | (A V B) V C ≡ A V (B V C) (A ˄ B) ˄ C ≡ A ˄ (B ˄ C) |

Distributive property for conjuctions/disjunctions | A V (B ˄ C)≡ (AVB)˄(AVC) A ˄ (B V C)≡ (A˄B)V(A˄C) |

Created by:
kgkasper