lessons

• This module was designed and written with you in mind. It is here to help you master about Sets. The scope of this module permits it to be used in many different learning situations. The language used recognizes the diverse vocabulary level of students. The lessons are arranged to follow the standard sequence of the course. But the order in which you read them can be changed to correspond with the textbook you are now using.
• Lessons in this module

  • Lesson 1 - Fundamentals of Sets
  • Lesson 2 - Set Notations
  • Lesson 3 - Relationship among Sets
  • Lesson 4 - Set Operations
• Set


  A collection of well-defined distinct objects
• Element

  The individual objects in a set
• Cardinality


  The total number of elements in a set
• Types of sets


  • Empty set
  • Finite set
  • Infinite set
• Empty/Null set


  A set with no elements
• Finite set


  A set with a definite number of elements
• Infinite set


  A set with an infinite number of elements
• A null set or empty set is also a finite set
• A collection is finite or infinite if and only if it is a well-defined collection
• Every element in a set is separated by a comma
• Months with 31 days

  • January
  • March
  • May
  • July
  • August
  • October
  • December
• Multiples of 8


  • 8
  • 16
  • 24
  • 32
  • 40
  • 48
  • 56
  • 64
  • 72
  • 80
  • etc.
• Climate seasons in the Philippines

  • Dry season
  • Wet season
• Delicious fruits in Cebu

  • Mango
  • Lanzones
  • Rambutan
  • Durian
  • Pomelo
• Vowels in the English alphabet


  • A
  • E
  • I
  • O
  • U
• Days in a week that start with T

  • Tuesday
  • Thursday
• Best beaches in the Philippines

  • Boracay
  • El Nido
  • Siargao
  • Coron
  • Panglao
• A collection is considered NOT well-defined if it is vague or not specific. What may appear to one person may not appear the same to another person.
• A null set or empty set is also a finite set.
• A collection is finite or infinite if and only if it is well-defined collection.
• Every element in the set is separated by a comma denoted by (,).
• n (⋃)


  Intersection of Sets: the set containing the common elements of two or more sets
• Denoted by ∩
• Sets


  • A
  • B
  • N
  • E
  • V
  • D
  • A
  • I
  • R
  • G
  • M
• A ∩ B


  {4, 5}
• n(A∩B)


  2
• A - B


  {1, 2, 3}
• n(A - B)


  3
• B - A


  {7, 8, 9}
• n(B - A)


  3
• Venn diagram is used to simply illustrate set operations such as intersection, union, and difference of two sets
• Repetition of elements is NOT allowed when writing in roster/listing method
• The cardinality of elements in a set is based on the number of elements in the set
• Union of Sets


  1. The set containing all the elements of two or more sets

  2. Denoted by ⋃
• A ⋃ B


  • {1, 2, 3, 4, 5, 7, 8, 9}
• n(A⋃B)


  8
• Sets


  • A = {4, 6, 8, 10, 12}
  • B = {5, 7, 9, 11, 13}
  • C = {5, 10, 15, 20}
  • D = {10, 20, 30}