Key things to understand before your Discrete Math Final

if I get an A im going to MOD pizza if not im killing myself

• ONLY IF -

P ONLY IF Q

• IS SUFFICIENT FOR -

P IS SUFFICIENT FOR Q

• IS NECESSARY FOR -

Q IS NECESSARY FOR P

DISJUNCTIVE SYLLOGISM

P V R

NEGATION P

—-

THEREFORE R

REAL NUMBERS INCLUDE..

ZEROS, SQUARES, SMALL DECIMAL NUMBERS, FRACTIONS, BASICALLY ANYTHING THAT ISNT A COMPLEX NUMBER

THE NEGATION of Ex Px is …

Ax NEG Px

THE NEGATION OF Ax Px is…

Ex NEG Px

IS ZERO A PERFECT SQUARE, & EVEN?

YES TO BOTH!!!

CARDINALITY |A|…

NUMBER OF ELEMENTS IN A SET. EITHER FINITE OR INFINITE. SQUARE BRACKETS ARE INFINITE!!

POWER SET 2^*

2 to the power of the elements in a set. double checks

IF U WANNA CONVERT FROM BINARY TO HEXI…..

CHOP INTO 4 NUMBERS EACH AND SOLVE THE EZ STYLE

Simple graph

each edge connects to two diff vertices, no two edges connect to the same pair or vertices

Multigraph

multiple edges can connect to the same vertices, but have NO FRUIT LOOPS!

Pseudograph

A multigraph, but with FRUIT LOOPS

Vertex is DEGREE 0

ISOLATED

Vertex is DEGREE 1

PENDANT

A SINGLE LOOP COUNTS AS…

2 DEGREES

SIMPLE paths & SIMPLE circuits

does NOT pass through the same edge twice, can pass through vertexs as needed

Connected path

you can travel anywhere

EULER path & EULER circuit

a simple path / circuit that connects EVERY EDGE

EULER CIRCUIT LIFEHACK

iF EACH VERTICES HAS AN EVEN DEGREE, then its a euler circuit

EULER PATH LIFEHACK

if no euler circuit, and if it has excatly two vertices with odd degrees, then its a euler path

HAMILTONIAN path & HAMILTONIAN circuit

simple path / circuit that passes through every vertex EXACTLY ONCE

HAMILTONIAN CIRCUIT LIFEHACK

if the number of vertices is 3 or higher, and the degree of every vertex is the number of vertices/2, then u have a hamiltonian circuit