CSC 245 Definitions Topics 15
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Discrete Mathematics
encompasses the representation and study of collections of distinct objects.

Philosophical Logic
the classical notion of 'logic'. The study of thought and reasoning.

Mathematical Logic
the use of formal languages and grammars to represent the syntax and semantics of computation

Wellformed formula (wff)
a correctly structured expression of a language

Proposition
a claim that is either true or false with respect to an associated context.

simple proposition
a proposition that contains no logical operators

compound proposition
a claim that is a combination of multiple propositions

Logically Equivalent
When two propositions both evaluate to the same result when given the same input

Tautology
a proposition that always evaluates to true

Contradiction
a proposition that always evaluates to false

Contingency
a proposition that is neither a tautology or a contradiction.

Logically Equivalent (def 2)
p and q are logically equivalent if p<>q is a tautology.

Predicate
A statement that includes one or more variables and will evaluate to either true or false when the variables are assigned values

Domain of Discourse
The collection of values from which a variable's value is drawn

Bound variable
A quantified variable in a predicate.

Free (Unbound) Variable
An unquantified variable

Argument
A connected series of statements to establish a definite proposition.

Inductive argument
Moves from specific observations to a general conclusion.

Deductive argument
Uses accepted general principles to explain a specific situation.

Valid deductive argument
(p1^p2^p3^...^pn)>q is valid if the conclusion must follow from the hypothesis.

Sound Argument
A valid argument that also has a true premises is a sound argument

Fallacy
an argument constructed with an improper inference

Conjecture
A statement with an unknown truth value

Theorem
a conjecture that has been shown to be true

Proof
A sound argument that establishes the truth of a theorem

Lemma
a simple theorem whose truth is used to construct more complex theorems

Corollary
a theorem whose truth follows directly from another theorem