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Discrete Mathematics
Definitions for midterm 1 @ humboldt
27
Computer Science
Undergraduate 2
10/04/2006

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Term
Statement:
Definition
A phrase that is either true or false
Term
Truth Table:
Definition
Displays all possible values and corresponding results.
Term
DeMorgan's Law:
Definition
Negation of a compound statement.
Term
Tautology:
Definition
A statement whos result is always true.
Term
Contradiction:
Definition
A statement whos results are always false.
Term
Argument:
Definition
A sequence of premesis, that if true, leads to a conclusion.
Term
Syllogism:
Definition
An argument that contains two premisis and a conclusion (with a term in common).
Term
Fallacy:
Definition
An error in reasoning which results in an invalid argument.
Term
Predicate:
Definition
Part of a sequence that gives information about the subject.
Term
Set:
Definition
collection of elements (objects).
Term
Element:
Definition
One of the items within a set.
Term
Subset:
Definition
Every element in a second set is within (comes from) an original set.
Term
Proper Subset:
Definition
A subset where the original set has at least one additional item.
Term
Contraposition:
Definition
Prove modus tollens instead of proving if P(x) then Q(x).
Term
The greeks:
Definition
Pythogoras -> a^2 + b^2 = c^2 / Theoreme -> sqrt(2) is irrational.
Term
Lemma:
Definition
a subsidiary preposition.
Term
Arab:
Definition
Conquered spain in 711bc.
Term
Al-Khowarizm
Definition
-> father of algebra and Algorithm -> came from his name.
Term
Dysjunctive Syllogism
Definition
P V Q
~Q
.:P
Term
Dysjunctive Addition
Definition
P V Q
P
.:R
Term
Modus Ponens
Definition
P -> Q
P
.:Q
Term
Modus Tollens
Definition
P -> Q
~Q
.:~P
Term
Conjunctive Simplification
Definition
P ^ Q
.:P
Term
Dilemma
Definition
P V Q
P -> R
Q -> R
.:R
Term
Contraposition in P then Q Form
Definition
P -> Q
~Q -> ~P
Term
Converse Error
Definition
P -> Q
Q -> P
Term
Inverse
Definition
P -> Q
~P -> ~Q
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