Flashcards
Logic and Proof 8.20.2021
Cards in this deck (30)
- 1proofLogical argument that uses a sequence of statements to prove a statement called a conjecture.
- 2theoremA proven statement or conjecture.
- 3conjectureAn educated guess that is based on known information.
- 4inductive reasoningReasoning that uses a number of specific examples to arrive at a plausible generalization of prediction.
- 5counterexampleA false example of a conjecture.
- 6statementAny sentence that is either true or false, but not both. Represented using \(p\) or \(q\).
- 7truth valueThe truth or falsity of a statement.
- 8negationA statement that has the opposite meaning as well as an opposite truth value. \(-p\), read "\(not\) \(p\)".
- 9compound statementWhen two or more compound statements are joined.
- 10conjunctionA compound statement formed by joining two or more statements with the word \(and\). \(p\) and \(q\). \(p\wedge q\)
- 11disjunctionA compound statement formed by joining two or more statements using the word \(or\). \(p\) or \(q\) \(p\vee q\)
- 12conditional statementA statement that can be written in \(if\)-\(then\) form. If \(p\) then \(q\). \(p \rightarrow q\)
- 13hypothesisThe phrase immediately following the word \(if\) in a conditional statement.
- 14conclusionThe phrase immediately following the word \(then\) in a conditional statement.
- 15logically equivalentStatements with the same truth values.
- 16biconditionalBoth the conditional statement and its converse are true.
- 17converseA statement formed by switching the hypothesis and the conclusion.
- 18deductive reasoningUses facts, rules, definitions, or properties to reach logical conclusions.
- 19Law of SyllogismIf \(p \rightarrow q\) and \(q \rightarrow r\) are true, then \(p \rightarrow r\) is also true.
- 20Law of DetachmentIf \(p \rightarrow q\) is true, then \(q\) is also true.
- 21postulate (axiom)A statement that is taken to be true without proof.
- 22reflexive propertyFor every number \(a\), \(a=a\).
- 23transitive propertyFor all numbers \(a\), \(b\), and \(c\), if \(a=b\) and \(b=c\), then \(a=c\).
- 24symmetric propertyFor all numbers \(a\) and \(b\), if \(a=b\), then \(b=a\).
- 25Addition and Subtraction PropertiesFor all numbers \(a\), \(b\), and \(c\), if \(a=b\) then \(a+c=b+c\) and \(a-c=b-c\).
- 26Multiplication and Division PropertiesFor all numbers \(a\), \(b\), and \(c\), if \(a=b\) then \(a \cdot c=b \cdot c\) and if \(c \neq 0\), \(\frac{a}{c}=\frac{b}{c}\).
- 27Substitution PropertyFor all numbers \(a\) and \(b\), if \(a=b\), then \(a\) may be replaced by \(b\) in any equation or expression.
- 28Distributive PropertyFor all numbers \(a,b\) and \(c\), \(a(b+c)=ab+ac\).
- 29Deductive argumentA group of algebraic steps to solve problems.
- 30two-colunn proof (formal proof)A proof that contains statements and reasons organized in two columns: statements and reasons.
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- High School Geometry Flashcards on Logic and Proof 8.20.2021, created by Theresa Cobb on 20/08/2021.
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