Language of Sets Flashcards
he played a pivotal role in the creation of set theory, which has become a fundamental theory in mathematics
George Cantor
are collections of well-defined distinct objects, ideas, or numbers.
Sets
sets consists of objects, called the ______ or the member of a set that share a common characteristic.
Element (∈)
a set is named by using a ?
capital letter
∈
belongs to
∉
does not belong to
: or |
such that
ɸ
null set, empty set
n(A)
cardinal number of the set A
∪
union of two sets
∩
intersection of two sets
a set that has a definite number of elements
elements are countable
Finite Set
is a set that contain endless number of elements
(…) ellipsis indicated after the last identifies element means that there a re other elements of the set
Infinite Set
a set with no elements
denoted by ɸ or {}
null set
The __________ of a set A is the number of elements contained in A. Denoted by |A| or n(A)
Example: A = {1, 2, 3, 4, } |A| = 4
B = {a, e, i, o, u} n(B) = 5
Cardinality
Is the set that contains all objects under consideration.
A set of all possible elements under consideration in a particular problem
Universal Set (U)
If all the elements of a Set F are also the elements of a Set A, then “F is a _____ of A
(F 드 A)
Subset (드)
A ____________ of a set A is a subset of A that is not equal to A. In other words, if B is a proper subset of A, then all elements of B are in A but A contains at least one element that is not in B.
proper subset
Two sets A and B are equal set if A C B and BCA. The elements of A are also the element of B
Equal Set
Two sets A and B are _________ set if the number of elements in set A is equal to the number of elements in set B. The cardinality of A and B are equal.
equivalent set
A mathematical diagram representing sets as circles, with their relationship to each other expressed through their overlapping positions, so that all possible relationship between the sets are shown.
Venn Diagram
The union of Set A and B is the set whose elements are those which belongs to Set A, or to Set B, or to both sets. In symbol, the union of set A and B is
A U B
The intersection of Set A and B is the set whose elements are common to Set A and to Set B. In symbol, the intersection of set A and B is
A ∩ B
The compliment of Set A is the set whose elements are elements of the universal set that does not belong to A. In symbol, the complement of A is
A’
All elements which are in A but not in B
A-B
is the most indispensable tool in solving word problems involving set, since it will help in visualizing the problems.
Venn Diagram
