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**Chapter 2**Sets**• Methods to indicate sets, equal sets, and equivalent**sets • Subsets and proper subsets • Venn diagrams • Set operations such as complement, intersection, union, difference and Cartesian product • Equality of sets • Application of sets • Infinite sets WHAT YOU WILL LEARN**Section 1**Set Concepts**Set**• A collection of objects, which are called elements or members of the set. • Listing the elements of a set inside a pair of braces, { }, is called roster form. • The symbol , read “is an element of,” is used to indicate membership in a set. • The symbol means “is not an element of.”**Well-defined Set**• A set which has no question about what elements should be included. • Its elements can be clearly determined. • No opinion is associated its the members.**Roster Form**• This is the form of the set where the elements are all listed, separated by commas. Example: Set A is the set of all natural numbers less than or equal to 25. Solution: A = {1, 2, 3, 4, 5,…, 25} The 25 after the ellipsis indicates that the elements continue up to and including the number 25.**Set-Builder (or Set-Generator) Notation**• A formal statement that describes the members of a set is written between the braces. • A variable may represent any one of the members of the set. Example: Write set B = {2, 4, 6, 8, 10} in set-builder notation. Solution: The set of all x such that x is a natural number and x is an even number 10.**Finite Set**• A set that contains no elements or the number of elements in the set is a natural number. Example: Set S = {2, 3, 4, 5, 6, 7} is a finite set because the number of elements in the set is 6, and 6 is a natural number.**Infinite Set**• An infinite set is a set where the number of elements is not a natural number; that is, you cannot count the number of elements. • The set of natural numbers is an example of an infinite set because it continues to increase forever without stopping, making it impossible to count its members.**Equal Sets**• Equal sets have the exact same elements in them, regardless of their order. • Symbol: A = B • Example: { 1, 5, 7 } = { 5, 7, 1 }**Cardinal Number**• The number of elements in set A is its cardinal number. • Symbol: n(A) • Example: A = { 1, 5, 7, 10 } n(A) = 4**Equivalent Sets**• Equivalent sets have the same number of elements in them. • Symbol: n(A) = n(B) • Example: A = { 1, 5, 7 } , B = { 2, 3, 4 } n(A) = n(B) = 3 So A is equivalent to B.**Empty (or Null) Set**• The null set (or empty set )contains absolutely NO elements. • Symbol:**Universal Set**• The universal set contains all of the possible elements which could be discussed in a particular problem. • Symbol: U**CourseSmart**Page 50