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# Intro to Geometry

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

Logic | The study of reasoning. Allow us to determine if a statement is true, false, or uncertain. |

Open Sentence | Contains no truth value. Contains a variable. |

3x+2=7 | Open Sentence |

10+4=15 | Closed Sentence |

Hannah has blue eyes. | Closed Sentence |

She has blue eyes. | Open Sentence |

Negatation | (~) place not in the statement or remove it. A statement and it's negatation have opposite truth values. |

Conjunction | Compound sentence formed by using and. (^) Only true when both parts are true. |

Disjunction | A compound sentence formed by using or (v) Only false when both parts are false. Only needs at least one true. |

Conditional | A compound sentence using if....then or implies (➡) |

Biconditional | (p ➡ q)^(q ➡ p) if and only if or (p ⬅➡ q) True when both parts match. |

Hypothesis | Follows if |

Conclusion | Follows then |

Consiquent | Another word for conclusion |

Compound Statement | T,F,T,F Sentence that is a mixture of true and false |

Tautology | Compound sentence that is always going to be true T,T,T,T |

Logically Equivalent | 2 statements that always have the same truth value. If it is logically equivalent it is tautology. |

Law of Detachment | R ➡ ~W R ________ ~W |

Conditional (original) | P ➡ Q |

Converse | Q ➡ P Switch |

Inverse | ~P ➡ ~Q Negate |

Contrapositive | ~Q ➡ ~P Switch and Negate |

A conditional and it's contrapositive always have same truth value | Logically Equivalent |

The converse and its inverse always have the same truth value | Logically Equivalent |

Law | Any thing that is true |

Given/ Premise | Always true |

Modus Tollens | A conditional Premise Negation of the Conclusion ____________________________ Conclude Negation of Hypothesis |

What is the difference between Law of Detachment and Modus Tollens? | In law of deatchment same symbols line up. P➡Q P ______ Q |

Modus Tollens= | Contrapositive and Law of Detachment |

Created by:
Naylor