Chapter 2 sets
ellipsis
"..." describe elements of a set tha continue in the same matter
"And" is generally interpreted to mean
"intersection.", The intersection of sets A and B, symbolized by A ∩ B, is the set containing all the elements that are common to both set A and set B.
what is a set?
A set is a collection of objects whose contents can be clearly determined.
Description
Describe elements of a set
Name the common methods to indicate a set:
Description, Roster form and set-builder notations
Two sets with no elements in common are called
Disjoint sets
cardinal number
Is the number of elements in a set
The set of elements common to both set A and set B is called
The set of elements common to both set A and set B is called the intersection of sets A and B, and is symbolized by A ∩ B. This definition can be expressed in set-builder notation as follows: A∩B ={x|x∈A and x∈B}
equal sets
Two sets are equal if they contain the same elements, any sets that are equal must also be equivalent.
what are the objects of a set called?
elements or members
Disjoint sets
two sets are said to be disjoint sets if they have no element in common.
infinite set
A set that is not finite is called an infinite set. The set of counting numbers is one example of an infinite set, because the number of counting numbers is not a natural number.
Equivalent sets
Equivalent sets have different elements but have the same amount of elements. ... A set's cardinality is the number of elements in the set. Therefore, if two sets have the same cardinality, they are equivalent!
Subset / proper Subset
If all the elements of set A are also elements of set B, then set A is a subset of set B. The statement that set A is a subset of set B is symbolized by A is a subset of ⊆ B. If it is also true that set A ≠set B, then set A is a proper subset of set B.
Complement of Set A
The complement of a set A is the set of all elements in the universal set that are not in A. This is symbolized by A′.
Empty Set
The empty set, also called the null set, is the set that contains no elements. The empty set is represented by { } or empty set∅.
The expression for determining the number of distinct subsets for a set with n distinct elements is:
The expression for determining the number of distinct subsets for a set with n distinct elements is 2ⁿ. Note that, since every set is a subset of itself, but no set is a proper subset of itself, the number of distinct proper subsets for a set with n distinct elements is 2ⁿ−1.
The three ways a set can be written are?
The three ways a set can be written are description, roster form, and set-builder notation. Writing a description of the set containing the elements Red, Blue and Yellow could be "The set is the primary colors." Expressing "Set C is the set of primary colors" in roster form could be C={Red, Blue, Yellow}. Writing the set containing the elements Red, Blue and Yellow in set-builder notation could be C={x|x is a primary color}.
Two sets that contain the same number of elements are called?
equivalent
A set that either contains no elements or the number of elements in the set is a natural number is called?
finite set
what is a well defined set?
if its content can be clearly determined
A set that is not finite is called a?
infinite set
Roaster Form
list the element inside a pair of braces
The set of all possible ordered pairs of the form (a,b), where a∈A and b∈B, is called the
the Cartesian product of set A and set B. It is symbolized AXB and is read "A cross B".
A set that contains all the elements for any specific discussion is called a?
universal , When a universal set is given, only the elements in the universal set may be considered when working a problem. If, for example, the universal set for a particular problem is defined as U={1, 2, 3, 4, ..., 10}, then only the natural numbers 1 through 10 may be used in that problem.