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Unformatted text preview: CMPSC 40: Foundations of Computer Science Key Terms & Results Peter Cappello Department of Computer Science University of California, Santa Barbara 1 T HE F OUNDATIONS : L OGIC & P ROOFS T ERMS proposition: a declarative statement that is true or false, but not both propositional variable: a variable that represents a proposition p (negation of p ): the proposition with truth value opposite to the truth value of p logical operators: operators used to combine propositions compound proposition: a proposition constructed by combining propositions using logical operators p q (disjunction of p and q ): the proposition p or q , which is true if and only if at least 1 of p and q is true p q (conjunction of p and q ): the proposition p and q , which is true if and only if both p and q are true p q ( p implies q ): the proposition if p then q , which is false if and only if p is true and q is false p q (biconditional): the proposition p if and only if q , which is true if and only if p and q have the same truth value p q (exclusive or of p and q ): the proposition p XOR q , which is true when exactly 1 of p and q are true converse of p q : q p inverse of p q : p q contrapositive of p q : q p tautology: a compound proposition that always is true contradiction: a compound proposition that always is false predicate: the part of a sentence that attributes a property to the subject propositional function: a statement containing 1 or more variables that becomes a proposition when each of its variables is assigned a value or is bound by a quantifier domain (or universe) of discourse: the set of values a variable in a propositional function may take xP ( x ) (existential quantification of P ( x ) ): the proposition that is true if and only if there exists an x in the domain such that P ( x ) is true xP ( x ) (universal quantification of P ( x ) ): the proposition that is true if and only P ( x ) is true for every x in the domain free variable: a variable not bound in a proposition function bound variable: a variable that is quantified 2 scope of a quantifier: part of a statement where the quantifier binds its variable argument: a sequence of statements argument form: a sequence of compound propositions involving propositional variables premise: a statement, in an argument or argument form, other than the final one conclusion: the final statement in an argument or argument form valid argument form: a sequence of propositions involving propositional variables where the truth of all the premises implies the truth of the conclusion valid argument: an argument with a valid argument form rule of inference: a valid argument form that can be used in the demonstration that arguments are valid fallacy: an invalid argument form theorem: a mathematical assertion that can be shown to be true conjecture: a mathematical assertion proposed to be true, but that has not been proven...
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This note was uploaded on 03/01/2009 for the course CS 40 taught by Professor Dam during the Spring '04 term at UCSB.
 Spring '04
 Dam
 Computer Science

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