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finite math


undefined, object
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all of whose elements are contained in S
- A is a subset of S if every element of A in contained in S

Set (S)

collection of items called 'elements'

can be a list or a rule/property

cartesian product

A x B, set of all ordered pairs where a is an element of A and b is an element of B (multiply)


set of elements in U that are not contained in A

counting elements of a set

we denote the number of elements in a set by using n(S)

counting principle for cartesian product
n(AxB)=n(A) x n(B)
multiplication principle

A={wheat, pumpernickel, rye}
B={turkey, ham} 
then the set of all possible sandwiches is the cartesian product AxB

de Morgan's laws

the complement of A intersect B is equal to the complement of A union B

the complement of A union B is equal to the complement of A intersect B

(can be extended to more than two s

disjoint sets

A and B are disjoint if they have no elements in common

distributive laws

(A intersect B) union C= (A union C) intersect (B union C)

(A union B) intersect C= (A intersect C) union (B intersect C)

factorial notation
7!= 7 x 6 x 5 x 4 x 3 x 2 x 1
(read 7 factorial)
0!= 1

P(90, 6)= 90x89x88x87x86x85

flipping a coin

two possible outcomes (heads or tails)


negative, zero, or positive whole number


set of elements contained in both A and B

partition (addition) principle

if a set X is partioned into sets X1 X2 etc, then:
n(X)=n(X1)+n(X2).. etc

partition of a set

So, A B and C are a partition of S

when you want to consider all possible arrangements of a set

how can you arrange ABCD? 
4 x 3 x 2 x 1 or 4!

measure of the likelihood that an event will occur

flipping a fair coin: probablity=.5
rolling a die: probability= 1/6

sample space

the outcomes of an experiment
(form a set)


set of elements in A, B, or both

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