# Study sets matching "discrete math"

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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…

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

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…

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…

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…

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…

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.

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

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…

1. Acute Angle

2. Adjacent Angles

3. Area

4. Circle

An angle with a measure of less than 90 degrees.

Angles that share a common side and a common vertex.

The space within a closed plane figure, measured in square uni…

The set of all points in a plane that are equidistant from a c…

1. Acute Angle

An angle with a measure of less than 90 degrees.

2. Adjacent Angles

Angles that share a common side and a common vertex.

Permutation is how many arrangements an…

1

A traveler can choose from three airlin…

Sequence

What is the difference between permutation and combination?

Compute ₅P₀

Multiplication Principle

An ordered list of numbers

Permutation is how many arrangements an…

What is the difference between permutation and combination?

1

Compute ₅P₀

composite

prime

substituted

predicate

合成关系, 合成数;... An integer n is prime if, and only if, n>1 and for…

素数, 质数;

vicarious;... When an element in the domain of the variable of a…

a sentence that contains a ﬁnite number of variables and becom…

composite

合成关系, 合成数;... An integer n is prime if, and only if, n>1 and for…

prime

素数, 质数;

What is a function?

Why is the codomain and domain necessar…

How is the vertical line test related t…

What are injective functions?

a function is simply a relation between a set of inputs and a…

let f be the function from x maps to x^2 -- why is this an inc…

Can test whether or not each x input maps to exactly one y inp…

The function is injective (one-to-one) if every element of the…

What is a function?

a function is simply a relation between a set of inputs and a…

Why is the codomain and domain necessar…

let f be the function from x maps to x^2 -- why is this an inc…

Statement

Simple statement

AND

OR

Sentence or mathematical expression that is either definitely…

Statement with single idea... Ex) every integer is a real number

Conjunction.... Connects 2 statements.... Symbol: ^... Ex) P ^ Q

Disjunction.... Connects 2 statements.... Symbol: v ... Ex) P v Q

Statement

Sentence or mathematical expression that is either definitely…

Simple statement

Statement with single idea... Ex) every integer is a real number

What is a digraph?... [Digraphs]

What is a path?... [Digraphs]

What is a simple path?... [Digraphs]

What is a cycle?... [Digraphs]

Directed Graph... Binary relation, R on A: R ⊆ A x A with direct…

Sequence of vertices connected with edges from vertex A to ver…

No repeated vertices

A path that starts and ends on the same vertice

What is a digraph?... [Digraphs]

Directed Graph... Binary relation, R on A: R ⊆ A x A with direct…

What is a path?... [Digraphs]

Sequence of vertices connected with edges from vertex A to ver…

Number Sequence

Arithmetic Sequence

Geometric Sequence

Binary Sequence

arrangement of numbers; follows the last according to a rule

adding the same numbers

multiplying by the same numbers

1,2,4,8,16

Number Sequence

arrangement of numbers; follows the last according to a rule

Arithmetic Sequence

adding the same numbers