Discrete Structures

Question 1

All elements of the universal set, minus the elements of the set under consideration

Answer 1

Absolute Compliment

Aᶜ

Question 2

The set of all possible ordered pairs between two sets

Answer 2

Cartesian Product

A x B

Question 3

The number of elements in a set

Answer 3

Cardinality

| A + B |

Question 4

A function from A to B that is also a function from B to A (must be both One-to-One and Onto for this to be true)

Answer 4

Invertible (Bijection)

Question 5

A series of functions linked together where the codomain of one function is the domain of the next function

Answer 5

Composite Function (Composition)

Question 6

Sets that have no common elements

Answer 6

Disjoint

Question 7

An item in a set

Answer 7

Element

∈

Question 8

A set of ordered pairs depicting all relations between the domain and codomain of a function

Answer 8

Graph

Question 9

The output element of a function for a given input

Answer 9

Image

Question 10

A relation between two sets in which every element of the domain is related to one element of the codomain

Answer 10

Function

ƒ()

Question 11

The set of all possible subsets for a single set

Answer 11

Power Set

2ᴬ; 2ᴮ; 2ᶜ etc…

Question 12

The set of elements that two or more sets have in common

Answer 12

Intersection

∩

Question 13

A function that maps each element of the domain to only one element in the codomain

Answer 13

One-to-one (Injection)

Question 14

A relation in which each element is related to itself

Answer 14

Reflexive

Question 15

The set of all image values of a function

Answer 15

Range

Question 16

A function in which every element of the codomain is mapped from an element of the domain

Answer 16

Onto (Surjection)

Question 17

If every element of one set is also an element of a second set

Answer 17

Subset

⊆

Question 18

A list of items that have something in common

Answer 18

Set

Question 19

A set of ordered pairs a directed graph can illustrate

Answer 19

Relation

Question 20

A set operation that results in a set containing the elements that remain when the second set is subtracted from the first set

Answer 20

Relative Complement

\

Question 21

The elements that belong to set A or set B but not both

Answer 21

Symmetric Difference

⊕

Question 22

A relation in which the first element related to the second element and the second element related to the third element implies the first element is also related to the third element

Answer 22

Transitive

Question 23

A graphical representation of sets as enclosed areas of a plane that shows all possible relationships

Answer 23

Venn Diagram

Question 24

The set operation that combines the elements of two or more sets

Answer 24

Union

∪

Question 25

A relation in which the first element is related to the second and the second element is related back to the first

Answer 25

Symmetric

Question 26

Every element of a set is in a second set but there is at least one element in the second set not in the first set.

Answer 26

Proper Subset

⊂

Question 27

The set with no elements

Answer 27

Empty Set or Null Set

∅ or {}

Question 28

A device that shows the truth value of a compound proposition for all combinations of input values

Answer 28

Truth Table

Question 29

A declarative statement that is either true or false but not both

Answer 29

Proposition

Question 30

The logical operator that results in a true output if one or the other or both propositions are true

Answer 30

OR

Question 31

The related form that negates the hypothesis and conclusion of a conditional statement and is not logically equivalent to the original conditional statement

Answer 31

Inverse

Question 32

The related form that reverses the order of the conditional statement and is not logically equivalent to the original conditional statement

Answer 32

Converse

Question 33

Each proposition that makes up an argument in a proof

Answer 33

Premise

Question 34

The logical operation that results from stating “if this then that”

Answer 34

Conditional

Question 35

The logical operation that results in a true output if one or the other but not both propositions are true

Answer 35

Exclusive OR

Question 36

The principle that describes a function with a finite domain graphed to a smaller finite codomain

Answer 36

Pigeonhole Principle

Question 37

The counting rule applied to non-intersecting sets of outputs

Answer 37

Sum Rule

Question 38

Sub propositions joined by logical connectives

Answer 38

Compound Proposition

Question 39

The counting rule applied to intersecting sets of outputs

Answer 39

Product rule

Question 40

The logical operation that results from stating “it is false that…”

Answer 40

NOT

Question 41

Validation of a conclusion from an argument based on the truth of the hypothesis

Answer 41

Proof

Question 42

A proposition that results in true for all inputs

Answer 42

Tautology

Question 43

The related form that reverses the order of and negates the hypothesis and conclusion of the conditional statement and is logically equivalent to the original conditional statement

Answer 43

Contrapositive

Question 44

The logical operator that results in a true output only if both propositions are true

Answer 44

AND

Question 45

The logical operation that results from stating “this if and only if that”

Answer 45

Biconditional

Question 46

A proposition that results in false for all inputs

Answer 46

Contradiction

Question 47

The condition where two propositions result in identical truth tables

Answer 47

Logically equivalent