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Math 61 Midterm 1

Terms in this set (29)

set
collection of distinct objects where order doesn't matter
element
object in a set
subset
X is a subset of Y if every element in X is an element in Y
empty set
a set with no elements
union of X and Y
set of elements in X or Y or both
intersection of X and Y
set of elements in both X and Y
powerset
P(X) is the set of all possible subsets of X
ordered list
sequence of objects with order taken into account
string over X
finite ordered list whose elements all come from X
n-tuple
ordered list of length n
ordered pair
ordered list of length 2
Cartesian Product
set of all n-tuples such that each n-tuple is (x1, x2, x3,...,xn)
function
a subset of XxY such that for all x from X there is exactly one y from Y so that (x,y) is in the function
one-to-one/injective
for all x1 not equal to x2, f(x1) is not equal to f(x2)
(each x has a unique y)
onto/surjective
function's codomain = range
bijective function/bijection
function that is one to one and onto
(each x has exactly one y, y has one x)
relation
R from X to Y is a subset of XxY
relation on X
relation from X to X
reflexive
if for all x in X, xRx
symmetric
if for all x,y in X, xRy and yRx
antisymmetric
if for all x,y in X, if xRy and yRx then x=y
transitive
if for all x,y,z in X, if xRy and yRz then xRz
equivalence relations
relations that are reflexive, symmetric, transitive
partial orders
relations that are reflexive, antisymmetric, transitive
equivalence class
set of all y in X such that xEy
partition P of set X
set of nonempty subsets of X such that every x in X is in exactly one set in P
permutation
way of ordering elements in a set
r-permutation
list of r-many elements in a set in order
(P(n,r) = n!/(n-r)!)
r-combination
choice of r-many elements from the set where order doesn't matter
(C(n,r) = n!/(r!(n-r)!))
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