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Chapter Two

Reasoning and Proof

TermDefinition
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