Subsets

• The empty set, denoted by {} or ∅, has no members.
• A subset is any set that contains only elements from another set
• A subset is any collection of elements that are also part of the original set.
• To show that A is a subset of B, we write A ⊆ B
• In the collection set are 69 well defined distinct objects. The objects contained in the sets are called elements
• Sets are denoted by uppercase letters of the alphabet
• Well defined set

  • The set of odd numbers between 1 and 15
  • Not well defined set: The set of pretty ladies in grade ?
• A set is defined if it must be given a collection of objects
• Set notation is using curly braces {} which are used to essentially list the objects in the set
• Sets are named using capital letters
• Ways of describing sets

  • Verbal description method: The set is defined in words using verbal statement
  • Roster or listing method: the elements of the set are listed using commas and enclosed in curly braces
• A subset is a "Part of the set" and can be smaller or equal in size to the original set, but they cannot have extra elements
• Subset

  Part of the set that is contained within the larger set
• The formula for the number of subsets of a set containing n Elements is 2^n
• A proper subset is a subset of a larger set that contains fewer members while still including unique elements
• Types of sets

  • Finite set - the set has a limited number of elements
  • Infinite set - A set has unlimited or accountable number of elements
  • Empty or null set - a set with no elements
• Cardinality of a set

  The number of elements in a mathematical set. It can be finite or infinite.
• The cardinality of the set {BLUE, YELLOW, RED, WHITE} is 4
• Set b

  Cardinality = {1, 3, 5, 7, 93}
• Set c

  x is composite number, 3 is infinite
• Set of natural numbers

  Infinite
• The set of whole numbers from 0 to 10
• Set a

  Even prime numbers greater than 2
• Set of all whole numbers

  Universal set
• The concept of union and intersection of sets is always a part of our daily life
• In going to school, you may pass through an intersection of two streets
• Union of two sets A and B

  The set which consists of all elements either in A or in B or in both
• Intersection of two sets A and B

  The set of all elements common to both A and B
• Set operations

  • Union
  • Intersection
• Venn diagram is popularized by john venn in 1880's
• A venn diagram is a diagram that help us visualize the logical relationship between sets and their elements
• Typically uses in intersecting and non intersecting circle to denote the relationship between sets
• Venn diagram can be drawn an with an unlimited circle
• How to make a venn diagram

  1. Categorize all item into sets
  2. Draw rectangle and label its pair correction between the sets
  3. Draw the circles according to the number of categorized you have
  4. Place all the items in theplace all the items in the replace all the items in the relevant circle