Set Theory Flashcards
What is a set?
A set is a well defined collection of objects.
What are elements?
They are objects within a set
Show that a belongs to set A
a E A (E rep epsilon)
How to determine a subset
A is a subset of B, if every element of A is also an element of B (A c B)
How to know two sets are equal
(A = B)
What is a proper set
A proper set is when A is a subset of B and A is not equal to B (A c B ), (A=/B)
What is union of sets?
It is denoted by U/or
It is the combination of all elements in both sets
What is Intersection of sets
It is denoted by n/and
It reps the common elements in both sets
What is Set difference (A-B)
It is denoted by-/~
It is all the elements in A that are not in B
What is symmetric difference
It is the union between two set differences (A-B) U (B-A)
What is a complementary of a set
It is all the elements that are not in the subset of a Universal set
What is the Cartesian product
the Cartesian product of AxB, is the set of all ordered pairs (a,b)
This concept is useful in scenarios where we consider all possible combinations of elements from 2 sets
What is a power set
It is the set of all subsets of a set.
It is often used in decision-making problems where we need to consider all possible combinations of decisions.
What is a function?
A function from a set A to a set B is a rule that assigns to each element of A exactly one element of B. Functions are used to model relationships between quantities, such as the relationship between the price and demand of a product.
What is a relation?
A relation from a set A to a set B is a subset of the Cartesian product AxB. Relations are used to model connections between elements of different sets, such as relations between employees and their job roles.
