Discrete Structures Flashcards
All elements of the universal set, minus the elements of the set under consideration
Absolute Compliment
Aᶜ
The set of all possible ordered pairs between two sets
Cartesian Product
A x B
The number of elements in a set
Cardinality
| A + B |
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)
Invertible (Bijection)
A series of functions linked together where the codomain of one function is the domain of the next function
Composite Function (Composition)
Sets that have no common elements
Disjoint
An item in a set
Element
∈
A set of ordered pairs depicting all relations between the domain and codomain of a function
Graph
The output element of a function for a given input
Image
A relation between two sets in which every element of the domain is related to one element of the codomain
Function
ƒ()
The set of all possible subsets for a single set
Power Set
2ᴬ; 2ᴮ; 2ᶜ etc…
The set of elements that two or more sets have in common
Intersection
∩
A function that maps each element of the domain to only one element in the codomain
One-to-one (Injection)
A relation in which each element is related to itself
Reflexive
The set of all image values of a function
Range
A function in which every element of the codomain is mapped from an element of the domain
Onto (Surjection)
If every element of one set is also an element of a second set
Subset
⊆
A list of items that have something in common
Set
A set of ordered pairs a directed graph can illustrate
Relation
A set operation that results in a set containing the elements that remain when the second set is subtracted from the first set
Relative Complement
\
The elements that belong to set A or set B but not both
Symmetric Difference
⊕
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
Transitive
A graphical representation of sets as enclosed areas of a plane that shows all possible relationships
Venn Diagram
The set operation that combines the elements of two or more sets
Union
∪