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Desiree B.

Two sets are equal

if and only if they have the same elements.

Set

an unordered collection of objects

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empty set

the set consisting of no elements

subset

Given two sets A and B, A is a subset of B if every element of A is an element of B.

proper subsets

If A is a subset of B, but there is one or more elements in B that do not exist in A.

infinite

a set is infinite if it is not finite

Union

the set that contains those elements that are in A or B or Both.

Intersection

The set containing those elements that exist in both A and B

Disjoint

two sets are disjoint if their intersection equals an empty set.

Function

A function F from set A to set B is an assignment of a unique element bEB for each element aEA

Injunction

F is injective if whenever f(a1)=f(a2), we have a1=a2 for a1,a2EA

translation

two elements A cannot map to the same b via f

Image

The subset of B that consists of all of the images of f is called the range, or image of f.

Surjection

F is surjective if for every bEB, we can find an aEA such that f(a)=b

Power Sets

Given a set A, we define the power set A to be the set that contains all subsets of A.

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Difference Sets

the difference sets A - B, consists of the elements that are not in A and are not in B

Sequence

A sequence of elements chosen from some sets is a function from N to S where N is an element of all natural numbers

Summation

given a sequence f:N>S, whose function values are summative, we can form a summation

Literal

A boolean variable or its compound

Minterm

A product of literals. One for each xi, xi bar, or xn.

Size of a Set

Given a set A with n distinct elements NEN, we say that A is a finite set and that the cardinality of the set is n.

Cartesian Product

The product of two sets, denoted AxB, is the set of all ordered pairs (a,b) where aEA and bEB

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