All Discrete Mathematic Terms

Discrete Mathematics

The study of mathematical structures that are fundamentally discrete rather than continuous.

Discrete Objects

Those which are separated from (not connected to/distinct from) each other.

Propositional Logic

Branch of mathematics that studies the logical relationships between propositions.

Truth Table

The compilation of all possible scenarios in a tabular format.

Negation

The complement of a proposition.

Conjuction

represents and ^

Disjunction

represents or V

XOR

High when 1 is odd.

Implication

Corresponds to If P then Q.

Biconditional

Corresponds to P if and only if Q.

Contrapositive

P implies Q, Thus Not Q implies Not P.

Converse

P implies Q, thus Q implies P.

Inverse

P implies Q, thus Not P implies Not Q.

Tautology

A proposition that is always true.

Universally Quantified Statement

Upside down A. True for every x in D.

Existentially Quantified Statement

For some x, P(x).

Argument

A set of two or more propositions related to each other in such a way that al but one of them are supposed to provide support for the remaining one.

Inference

Transition from premises to conclusion upon which the argument relies.

Premise

All but final proposition in the argument

Conclusion

Final proposition.

Valid

IF the truth of all its premises implies that the [conclusion is true.]

Set

A collection of definite and distinguishable objects selected by the means of certain rules or description. An unordered collection of different elements.

G. Cantor

German Mathematician, defined sets.

Set Theory

Forms the basis of several other fields of study like counting theory, relations, graph theory, etc.

Roster or Tabular Form

Set represented by listing all the elements comprising it.

Set Builder Notation

Giving distinguished property of the elements a set. Explicit desc of the set.

N

Set of Natural Numbers

Z

Set of all integers.

Z+

Set of all positive integers.

Q

set of all rational numbers.

R

set of all real numbers.

W

Set of all whole numbers.

Cardinal Number

number of elements in the set.

Finite Set

Sets that contain a definite number of elements.

Infinite Set

Sets that contain an infinite number of elements.

Subset

A set that contains all the elements within another set.

Proper Subset

Subset of but not equal to.

Universal Set

A collection of all elements in a particular context or application. Represented as U.

Empty Set or Null Set

A set with no elements.

Unit Set or Singleton Set

Set that contains only one element.

Equal Set

Sets that have the same elements.

Equivalent Set

Sets that have the same cardinal number.

Overlapping Set

Sets with one or more common element.

Disjoint Set

If two elements have nothing in common.

Venn Diagrams

Invented by John Venn. Shows all possible logical relations.

Function

A relation between sets A and B. Has an input and an output.

One to One or Injective Function

Every element of the domain has a single image with a range after mapping,

Many to One Function

One or more element in domain having a single range.

Onto (Surjective) Function

Every element of B is the image in some Element A.

Into Function

Every element of A is the image in some Element B.

Sequence

Set of numbers in a definite order according to some definite rules.

Nth Term

A rule that describes all the terms of a sequence.

Recursive Formula

A rule that describes the next term in the sequence.