# Study sets matching "discrete math"

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fundamental Counting Principle

Addition Principle

recursive definition

Fibonacci sequence

if one event can have x possible different outcomes, and after…

address situations in which two different tasks are completed…

whenever one element of a sequence is defined in terms of a pr…

0,1,1,2,3,5,8,13,21

fundamental Counting Principle

if one event can have x possible different outcomes, and after…

Addition Principle

address situations in which two different tasks are completed…

statement

negation of ¬p

conjunction p^q

conjunction

an expression which is either true or false

p... and goes to or... and p goes to ¬p... MAKES P NOT TRUE

AND... "p and q"... both HAVE to be TRUE

p^q

statement

an expression which is either true or false

negation of ¬p

p... and goes to or... and p goes to ¬p... MAKES P NOT TRUE

statement

negation of ¬p

conjunction p^q

conjunction

an expression which is either true or false

p... and goes to or... and p goes to ¬p... MAKES P NOT TRUE

AND... "p and q"... both HAVE to be TRUE

p^q

statement

an expression which is either true or false

negation of ¬p

p... and goes to or... and p goes to ¬p... MAKES P NOT TRUE

fundamental Counting Principle

Addition Principle

recursive definition

Fibonacci sequence

if one event can have x possible different outcomes, and after…

address situations in which two different tasks are completed…

whenever one element of a sequence is defined in terms of a pr…

0,1,1,2,3,5,8,13,21

fundamental Counting Principle

if one event can have x possible different outcomes, and after…

Addition Principle

address situations in which two different tasks are completed…

Propositions

We use propositional variables to

A propositional variable can have one o…

Usually are lower case letters starting…

Declarative sentence that can be... either true or false.

Refer to... propositions

true (T) or false (F)

p (i.e. p, q,... r, s, etc.)

Propositions

Declarative sentence that can be... either true or false.

We use propositional variables to

Refer to... propositions

Statement

Negation

Conjunction

Disjunction

A statement (proposition) is a sentence that is either true or…

A negation of a statement p is the statement "not p" or "it is…

The conjunction of two statements p and q is the statement "p…

The disjunction of two statements p and q is the statement "p…

Statement

A statement (proposition) is a sentence that is either true or…

Negation

A negation of a statement p is the statement "not p" or "it is…

preference ballot

preference schedule

plurality method

majority rule

a ballot in which the voters are asked to rank the candidates…

table that summarizes all of preference ballots

the candidate with the most first choice votes

the one with the majority (more than half of the votes)

preference ballot

a ballot in which the voters are asked to rank the candidates…

preference schedule

table that summarizes all of preference ballots

Bipartite Graph

Circuit

Complement Graph

Complete Graph

A graph whose vertices can be divided into 2 sets such that no…

A walk that begins and ends at the same vertex, and has no rep…

A graph with the same # of vertices as G but has an edge betwe…

A simple graph in which each pair of vertices is joined by an…

Bipartite Graph

A graph whose vertices can be divided into 2 sets such that no…

Circuit

A walk that begins and ends at the same vertex, and has no rep…

Gelly Roll pens come in 6 colors of fin…

When redeeming a prize coupon, you may…

Prove that if n is even, then n2 is eve…

Prove that if n is odd, then n2 +5n−3 i…

By the sum principle, 6+11+10+10+12+14= 63.

By the product and sum principles, 6 · 3 + 6 · 2 = 18 + 12 = 3…

Because n is even, we may write n=2k,and n=2k⇒n2 =4k2 =2(2k2).

Because n is odd, we may write n=2k+1, and n=2k+1⇒n2+5n−3= (2k…

Gelly Roll pens come in 6 colors of fin…

By the sum principle, 6+11+10+10+12+14= 63.

When redeeming a prize coupon, you may…

By the product and sum principles, 6 · 3 + 6 · 2 = 18 + 12 = 3…

algorithm

searching algorithm

linear search algorithm

binary search algorithm

a finite sequence of precise instructions for performing a com…

the problem of locating an element in a list

a procedure for searching a list of element by element

a procedure for searching an ordered list by successively spli…

algorithm

a finite sequence of precise instructions for performing a com…

searching algorithm

the problem of locating an element in a list

Irrational Numbers

Rational Numbers

Natural Numbers

Whole Numbers

do not terminate or repeat, cannot be written as a fraction

numbers that terminate or repeat, can be written as a fraction

Counting Numbers

0 and counting numbers

Irrational Numbers

do not terminate or repeat, cannot be written as a fraction

Rational Numbers

numbers that terminate or repeat, can be written as a fraction

Universal Statement

Conditional Statement

Give an example of universal statement

Give example of a conditional statements

A certain property i true for all elements in a set.

If one thing is true then some other thing also has to be true.

All positive numbers are greater than zero.

if a car is cheap then it is on sale

Universal Statement

A certain property i true for all elements in a set.

Conditional Statement

If one thing is true then some other thing also has to be true.

Proposition

Propositional variables (or statement v…

Compound propositions

p → q (Conditional Statement)

A proposition is a declarative sentence (that is, a sentence t…

We use letters to denote propositional variables (or statement…

The propositions formed from existing propositions using logic…

False only when p is True and q is False.... (Or)... Always True whe…

Proposition

A proposition is a declarative sentence (that is, a sentence t…

Propositional variables (or statement v…

We use letters to denote propositional variables (or statement…

isolated vertex

loop

parallel

adjacent

vertex unconnected by edge to any other vertex

edge that connects vertex to itself

two edges that connect the same pair of vertices

vertices that are connected by an edge

isolated vertex

vertex unconnected by edge to any other vertex

loop

edge that connects vertex to itself

Blind study

Capture-recapture method

Census

Chance error

study in which neither the members of the treatment group nor…

Step 1. Capture (sample): Capture (choose) a sample of size n1…

the process of collecting data by going through every member o…

the result of the basic fact that a sample, being just a sampl…

Blind study

study in which neither the members of the treatment group nor…

Capture-recapture method

Step 1. Capture (sample): Capture (choose) a sample of size n1…

statement

negation of ¬p

conjunction p^q

conjunction

an expression which is either true or false

p... and goes to or... and p goes to ¬p... MAKES P NOT TRUE

AND... "p and q"... both HAVE to be TRUE

p^q

statement

an expression which is either true or false

negation of ¬p

p... and goes to or... and p goes to ¬p... MAKES P NOT TRUE

Voting Theory

preference ballots

preference schedule

plurality method

understanding the intricacies of the voting process

voter ranks all candidates in order of preference

a table summarizing the ballots by grouping the identical ball…

the choice with the most first-preference votes is declared th…

Voting Theory

understanding the intricacies of the voting process

preference ballots

voter ranks all candidates in order of preference

Set Notation

Empty Set

Natural Numbers

Integers

"The set of all x in T such that P(x)";set of all objects of t…

{ }

N : The set of numbers 1, 2, 3, 4, ... Also called counting nu…

Z : All whole numbers (both positive and negative) and zero.

Set Notation

"The set of all x in T such that P(x)";set of all objects of t…

Empty Set

{ }

Lemma

Corollary

Parity

Modular Arithmetic

A helpful mini theorem that helps you prove your theorem

A proposition that follows from (and is often related too) one…

The fact of being even or odd

Given 2 positive numbers, a(the dividend) and n(the divisor),…

Lemma

A helpful mini theorem that helps you prove your theorem

Corollary

A proposition that follows from (and is often related too) one…

statement

negation of ¬p

conjunction p^q

conjunction

an expression which is either true or false

p... and goes to or... and p goes to ¬p... MAKES P NOT TRUE

AND... "p and q"... both HAVE to be TRUE

p^q

statement

an expression which is either true or false

negation of ¬p

p... and goes to or... and p goes to ¬p... MAKES P NOT TRUE