CS Notation Flashcards
a collection of elements
{ } Set
in A or B (or both)
A ∪ B Union
in both A and B
A ∩ B Intersection:
every element of A is in B.
A ⊆ B Subset:
every element of A is in B,but B has more elements.
A ⊂ B Proper Subset:
A is not a subset of B
A ⊄ B Not a Subset:
A has same elements as B, or more
A ⊇ B Superset
A has B’s elements and more
A ⊃ B Proper Superset:
A is not a superset of B
A ⊅ B Not a Superset:
elements not in A
A’ Complement:
in A but not in B
A − B Difference or A \ B
a is in A
a ∈ A Element of:
b is not in A
b ∉ A Not element of:
{}
Ø Empty set =
set of all possible values(in the area of interest)
U Universal Set:
all subsets of A
P(A) Power Set:
both sets have the same members
A = B Equality:
(set of ordered pairs from A and B)
A×B Cartesian Product
the number of elements of set A
|A| Cardinality:
Such that
| or :
or :
For All
∀
There Exists
∃
Therefore
∴
Divisible by
⋮
All Positive integers and 0
N natural number
Numbers that are not a fraction
Z integers
Any fraction with non zero denominators
Q rational numbers
Include rational numbers like positive and negative integers, fraction, and irrational numbers
R: real numbers
Empty String
Λ
To express that an element belongs to a set we use
∈
To express that an element does NOT belong to a set we use
∉
Collection of objects
Set
Well defined, un ordered and distinct collection of elements
Sets
each elements in the set satisfies a certain description
well dfined
does not follow a certain order of appearance
unordered
there could onyl be one item that has the element’s characteristic across the set
Distinct
the number of elements inside a set
Cardinality
2 ways of defining a set
Formal and Informal
Uses normal words, or enumeration to determine the members of a set
Informal definition
Use mathematical symbols and statemetns through induction to define what constitutes a particular set
Formal definition
Formal or informal:
a = {1, 2, 3, 5}
informal
Formal or Informal:
A = {Dog, Cat, Turtle, Cow}
Informal
Formal or informal:
x = {2k + 1| k ∈ N}
Formal
Formal or informal:
D = {students of Math class}
informal
The concept of formally defining sets is called??
Set builder notation
Combines components of 2 different sets
Union
Containing only the element that are common to bothsets mentioned
Intersection
Consists of all elements that are not in the subjected set
Complement
Set containing the element of the element in the left side not the right or the element of A not B.
Difference
Set containing the elements that are in either set BUT NOT BOTH
Symmetric difference
Symbol for Union
U
Symbol for Intersection
∩
Symbol of complement
’
Symbol of difference
\ or -
Symbol of symmetric difference
Δ
