Vocabulary
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| Inductive Reasoning | A type of reasoning that reaches conclusions based on a pattern of specific examples or past events.
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| Conjecture | A conclusion reached by using inductive reasoning
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| Counterexample | An example showing that a statement is false.
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| Conditional | A conditional is an if-then statment.
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| Hypothesis | In an if-then statement (conditional) the hypothesis is the part that follows if.
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| Conclusion | The conclusion is the part of an if-then statement (conditional) that follows then.
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| Truth Value | The truth value of a statement is "true" or "false" according to whether the statement
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| Negation | The negation of a statment has the opposite meaning of the original statement.
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| Converse | The statement obtained by reversing the hypothesis and conclusion of a conditional.
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| Inverse | The inverse of the consitional "if p, then q" is the conditional "if not p, then not q."
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| Contrapositive | The contrapositive of the conditional "if p, then q" is the conditional "if not q, the not p." A conditional and its contrapositive always have the same truth value.
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| Equivalent Statements | Statements with the same truth value.
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| Biconditional | A biconditional statement is the combination of a conditional statement and its converse. A biconditional contains the words "if and only if."
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| Deductive Reasoning | A process of reasoning logically from given facts to a conclusion.
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| Law of Detachment | If the hypothesis of a true conditional is true, then the conclusion is true.
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| Law of Syllogism | Allows you to state a conclusion from two true conditional statements when the conclusion of one statement is the hypothesis of the other statement.
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| Reflexive Property | A = A
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| Symmetric Property | If a = b then b = a
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| Transitive Property | If a = b and b = c, then a = c
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| Proof | A convincing argument that uses deductive reasoning.
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| Two-column proof | Lists each statement on the left. The justifcation, or the reason for each statement, is on the right. Each statement must follow logically from the steps before it.
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| Theorem | Is a conjecture that is proven.
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| Paragraph proof | A proof written as a paragraph.
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