Reasoning and Proof
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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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".
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If Then Statement | "If p, then q" where p and q are statements
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Hypothesis | In a conditional statement, the phrase IMMEDIATELY following the word "IF"
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conclusion | In a conditional statement, the phrase IMMEDIATELY following the word "THEN"
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related conditionals | statements that are based on a given conditional statement
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converse | Formed by exchanging the hypothesis and the conclusion of the conditional. If Q, then P
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inverse | formed by negating both the hypothesis and the conclusion of the conditional If -p then -q
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contrapositive | formed by negating both the hypothesis and the conclusion of the converse of the conditional If-q, then -p
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logically equivalent | Statements with the same truth values
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inductive reasoning | reasoning that uses a number of specific examples to arrive at a conclusion.
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conjecture | a concluding statement reached using inductive reasoning
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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.
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statement | a sentence that is either true or false
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truth value | a statement is either (T) true or (F) false
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negation | has the opposite meaning of a statement as well as the opposite truth value
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compound statement | two or more statements joined by the word "AND" or "OR"
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conjunction | a compound statement using the word "AND". It is only true when BOTH statements are true
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disjunction | a compound statement that uses the word "OR". It is true if at least ONE of the statements is true
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truth table | can be used to determine truth values of negations and compound statements
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deductive reasoning | uses facts, rules, definitions,or properties to reach logical conclusions from given statements.
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valid | logically correcty method of proving a conjecture
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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)
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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)
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postulate/axiom | statement that is accepted as true without proof
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proof | logical argument in which each statement you make is supported by a statement that is accepted as true
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Theorem | once a statement or conjecture has been proven. This can be used as a reason to justify statements in other proofs
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paragraph proof/informal proofs | writing a paragraph to explain why a conjecture for a given statement is true
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algebraic proof | proof that is made up of a series of algebraic statements
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two-column or formal proof | statements and reasons organized into two columns
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reflexive property | AB=AB(line segments)
measure of angle 1= measure of angle 1 (angles)
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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
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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.
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equivalence relation | any relationship that satisfies the Reflexive, Symmetric and Transitive Properties.
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Created by:
amgeometry
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