Ch. 1.1 | Sets & Subsets Flashcards
Element
Objects of the set. [or members of the set]
Empty Set
(or null set) denoted by { }, or Ø, is the set that has no elements.
Consider to be a subset of every set.
Equal Sets
( = ) “is the same as”
Two sets are equal if they are exactly the same set.
Sets with the same elements.
Equivalent Sets
Sets of the same size.
Equivalent Sets do not mean the same thing as Equal Sets. Equivalent Sets are sets that are in one-to-one correspondence
Member
Objects of the set. [or elements of the set]
Null Set
(or empty set) denoted by { }, or Ø, is the set that has no elements.
Consider to be a subset of every set.
One-to-one correspondence
Consider the set of boys called B = {Jack, Fred, Ron} and the set of girls called G = {Rhonda, Heather, Joy}. In a relay race, each element of set B is paired with one and only one element of set G.
Proper Subset
(A) is a proper subset of (B) if it is a subset of (B) other than (B) itself.
Denoted by the symbol ⊂.
Set
A collection of objects.
Denoted by braces { }, and is named with a capital letter.
Set Braces
Denoted by { }; used in describing elements of a set.
In the list method, the elements are listed inside set braces.
Set-builder Notation
The general form of “set-builder notation” is
{x | x is …}, where x is an arbitrary element of the set, and the vertical line, | , indicates the words “such that”.
The vertical line, | , is followed by a description of a representative element of the set.
Subset
Denoted by ⊆
A set of which all the elements are contained in another set
Universal set
Denoted by U
A set that contains the elements in the context of a given problem.
Venn Diagram
Helps illustrate the set relations.
