DISCRETE STRUCTURE 2 Flashcards
mathematician introduce the concept of set
G. cantor
George Cantor
{}
the set of
⊆
subset - its A = B or A is smaller than set B and the element of A are in B
∪
union - all set both A and B will write accordingly
A
the set of A
∩
intersect - all element that common to both set may pagka same?
a
element
⊄
not propersubset = if |A|=|B| but set A or B have one element that are not the same or if set A have element that dont have in set B
⊂
proper subset - if both set have same element and set A is smaller or set B
∈
is a member of A = {1,2,3} 123 is a member
2 kind of set
roster form
tabular form
what is set
unodered collection of different elements
∉
is not a member A = {1,2,3} 4 is not a member
:
such that
=
is
N is a set of?
all natural numbers
Z is a set of
all integers
Z+ is a set of
positive initegers
Q is a set of
rational numbers
R is a set of
real numbers
W is a set of
whole numbers
||
cardinality
cardinality means
number of elements
|S|
the cardinality of set S
S = {6,4,9,7,8} how many cardinality
5
3 approacher of cardinality
bijection injection and surjection
bijection define
if injection and surjection are approved its bijection same number in domain and codomain
surjection define
if domain have more cardinality than codomain A >= B
injection define
if one of the set is not mapped on the same value and the element not produce two possible output its injection and if domain have less cardinality in codomain A < B
denoted of cardinality give 4
(A). Ā. card(A). or #A
give type of set can be classified
finite, infinite, subset, universal, proper, singleton set, etc
combinatorics define
the mathematical counting and arranging for large number
pigeonhole define
its A > B or surjective its called pigeonhole because think of you have 4 pigeon and 3 holes imposibleng mag sakto lang yung sa pigeon kahit isa dun na ma hole magkakaron ng dalawwang pigeon
⊉
not proper superset - means the
|A|=|B| but one of the element is not the same or if element of B is not in the set A
⊃
proper superset - if set B have smaller element than a set A and all element in B has in A
⊇
superset - if A = B or set B is smaller and all elements in B are in A
