Chap 4

• Set is a collection of well defined objects
• Set is a mathematical way of representing a collection or a group of objects
• The objects of a set are called elements or members of the set
• Sets can be represented in two ways −  Descriptive form and Roster or Tabular Form
• Descriptive form is one way to specify a set is to give a verbal description of its element
• Roster or Tabular form is the set is represented by listing all the elements comprising it. The elements are enclosed within braces and separated by commas
• Set Builder Notation - The set is defined by specifying a property that elements of the set have in common. Is a notation for describing a set by indicating the properties that its members must satisfy
• “:” or “|” means such that
• N is the set of all natural numbers = {1, 2, 3, 4, .....}
• Z is the set of all integers = {....., −3, −2, −1, 0, 1, 2, 3, .....}
• Z+ is the set of all positive integers
• Q is the set of all rational numbers = {1.5, 2.5, 3.5, 4.5, .....}
• R is the set of all real numbers
• W is the set of all whole number = {0, 1, 2, 3, 4, .....}
• Ellipsis are used to indicate that the pattern of the listed elements continues
• Cardinality of a set is the number of elements of the set

  If a set has an infinite number of elements, its cardinality is ∞
• Cardinality of a set symbol is |S|
• Subset symbol is ⊆
• Proper Subset symbol is ⊂
• Universal Set symbol is U
• Empty set symbol is {} or ∅
• Singleton/Unit set symbol is {s}
• Set Union - A ∪ B = {x | x ∈ A OR x ∈ B}

  
• Set Intersection - A ∩ B = {x | x ∈ A AND x ∈ B}

  
• Set Difference/Relative Complement - A - B = {x | x ∈ A AND x ∉ B}

  
• Complement of a Set - A’ = = {x | x ∉ A} (U - A)

  
• Cartesian Product - A x B = {(a,1),(a,2),(b,1),(b,2)}
• Finite Set - a set which contains a definite number of elements
• Infinite Set - A set which contains infinite number of element
• Proper Subset - can be defined as “subset of but not equal to”
• Universal Set - It is a collection of all elements in a particular context or application. All the sets in that context or application are essentially subsets of this set
• Singleton Set or Unit Set - unit set contains only one element
• Equivalent Set - If the cardinalities of two sets are same
• Overlapping Set - two sets that have at least one common element
• Disjoint Set - are sets that do not have even one element in common
• Equal set - if the sets contains the same elements
• Empty Set or Null Set - An empty set contains no elements
• As the number of elements in an empty set is finite, empty set is a finite set. The cardinality of empty set or null set is zero
• Set Union - is the set of elements which are in A, in B, or in both A and B
• Set Intersection - is the set of elements which are in both A and B