CSC 245 Definitions Topics 1-5

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starscater
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199589
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CSC 245 Definitions Topics 1-5
Updated:
2013-02-10 23:16:40
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discrete math 245 mccann
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Definitions for Exam 1 review.
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  1. Discrete Mathematics
    encompasses the representation and study of collections of distinct objects.
  2. Philosophical Logic
    the classical notion of 'logic'.  The study of thought and reasoning.
  3. Mathematical Logic
    the use of formal languages and grammars to represent the syntax and semantics of computation
  4. Well-formed formula (wff)
    a correctly structured expression of a language
  5. Proposition
    a claim that is either true or false with respect to an associated context.
  6. simple proposition
    a proposition that contains no logical operators
  7. compound proposition
    a claim that is a combination of multiple propositions
  8. Logically Equivalent
    When two propositions both evaluate to the same result when given the same input
  9. Tautology
    a proposition that always evaluates to true
  10. Contradiction
    a proposition that always evaluates to false
  11. Contingency
    a proposition that is neither a tautology or a contradiction.
  12. Logically Equivalent (def 2)
    p and q are logically equivalent if p<-->q is a tautology.
  13. Predicate
    A statement that includes one or more variables and will evaluate to either true or false when the variables are assigned values
  14. Domain of Discourse
    The collection of values from which a variable's value is drawn
  15. Bound variable
    A quantified variable in a predicate.
  16. Free (Unbound) Variable
    An unquantified variable
  17. Argument
    A connected series of statements to establish a definite proposition.
  18. Inductive argument
    Moves from specific observations to a general conclusion.
  19. Deductive argument
    Uses accepted general principles to explain a specific situation.
  20. Valid deductive argument
    (p1^p2^p3^...^pn)->q is valid if the conclusion must follow from the hypothesis.
  21. Sound Argument
    A valid argument that also has a true premises is a sound argument
  22. Fallacy
    an argument constructed with an improper inference
  23. Conjecture
    A statement with an unknown truth value
  24. Theorem
    a conjecture that has been shown to be true
  25. Proof
    A sound argument that establishes the truth of a theorem
  26. Lemma
    a simple theorem whose truth is used to construct more complex theorems
  27. Corollary
    a theorem whose truth follows directly from another theorem

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