# finite math

## Terms

undefined, object
copy deck

subset

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)

complement

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
0!= 1

P(90, 6)= 90x89x88x87x86x85

flipping a coin

two possible outcomes (heads or tails)

integer

negative, zero, or positive whole number

intersection

set of elements contained in both A and B

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

partition of a set

S={0,1,2,3,4,5,6,7,8,9}
A={0}
B={1,3,5,7,9}
C={2,4,6,8}
So, A B and C are a partition of S

permutations
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!

probability
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)

union

set of elements in A, B, or both

19

jaclynrb4