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# Chapter Two

### Reasoning and Proof

Term | Definition |
---|---|

conditional statement | a statment that can be written in "if-then" form. Example: If you would like to speak to a customer service representative, then hit "O". |

If Then Statement | "If p, then q" where p and q are statements |

Hypothesis | In a conditional statement, the phrase IMMEDIATELY following the word "IF" |

conclusion | In a conditional statement, the phrase IMMEDIATELY following the word "THEN" |

related conditionals | statements that are based on a given conditional statement |

converse | Formed by exchanging the hypothesis and the conclusion of the conditional. If Q, then P |

inverse | formed by negating both the hypothesis and the conclusion of the conditional If -p then -q |

contrapositive | formed by negating both the hypothesis and the conclusion of the converse of the conditional If-q, then -p |

logically equivalent | Statements with the same truth values |

inductive reasoning | reasoning that uses a number of specific examples to arrive at a conclusion. |

conjecture | a concluding statement reached using inductive reasoning |

counterexample | If a conjecture is not true for all cases, the false example is called the counterexample. It can be a number, drawing or statement. |

statement | a sentence that is either true or false |

truth value | a statement is either (T) true or (F) false |

negation | has the opposite meaning of a statement as well as the opposite truth value |

compound statement | two or more statements joined by the word "AND" or "OR" |

conjunction | a compound statement using the word "AND". It is only true when BOTH statements are true |

disjunction | a compound statement that uses the word "OR". It is true if at least ONE of the statements is true |

truth table | can be used to determine truth values of negations and compound statements |

deductive reasoning | uses facts, rules, definitions,or properties to reach logical conclusions from given statements. |

valid | logically correcty method of proving a conjecture |

Law of Detachment | If p to q is a true conditional and p is true, then q is also true (As long as the given facts are true, the conclusion reached using deductive reasoning will also be true) |

Law of Syllogism | If p to q and q to r are true conditionals, then p to r is also true (You can draw conclusions from 2 true conditional statements when the conclusion of one statement is the hypothesis of the other) |

postulate/axiom | statement that is accepted as true without proof |

proof | logical argument in which each statement you make is supported by a statement that is accepted as true |

Theorem | once a statement or conjecture has been proven. This can be used as a reason to justify statements in other proofs |

paragraph proof/informal proofs | writing a paragraph to explain why a conjecture for a given statement is true |

algebraic proof | proof that is made up of a series of algebraic statements |

two-column or formal proof | statements and reasons organized into two columns |

reflexive property | AB=AB(line segments) measure of angle 1= measure of angle 1 (angles) |

symmetric property | If AB=CD, then CD=AB. (line segments) If the measure of angle 1= the measure of angle 2, then the measure of angle 2=the measure of angle 1 |

transitive property | If AB=CD and CD=EF, then AB=EF (line segment) If the measure of angle 1 = the measure of angle 2 and the measure of angle 2 = the measure of angle 3, then the measure of angle 1= the measure of angle 3. |

equivalence relation | any relationship that satisfies the Reflexive, Symmetric and Transitive Properties. |

Created by:
amgeometry