# Study sets matching "discrete math"

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…

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…

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…

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…

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.

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;

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

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 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…

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…

Inductive reasoning

Deductive reasoning

Conjecture

Theorem

Making a decision based on patterns and observation

Process of making a decision based on facts

...

...

Inductive reasoning

Making a decision based on patterns and observation

Deductive reasoning

Process of making a decision based on facts