Chapter Sets and Venn Diagrams A Set is a

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					                                   Chapter 1C - Sets and Venn Diagrams
                                                         Chapter 1C - Sets and Venn Diagrams
               A Set is a collection of objects. Elements of the set are the individual objects, e.g., if x is an
               element of a set S then we write x ∈ S . Sets are described by listing their members within
                                     }. Use three dots,. . ., to indicate a continuing pattern if there are too
               a pair of braces, { A Set is a collection of objects. Elements of the set are the individual objects, e
               many members to list. element of a set S then we write x ∈ S . Sets are described by listing their mem
                            - Sets braces, { }. Use Diagrams
                                          Venn Diagrams
                 Chapter 1C a pair of andand of Numbers dots,. . ., to indicate a continuing pattern if t
                   Chapter 1C - Sets Sets Venn three
                            many members to list.   Chapter 1C - Sets and Venn Diagra
                    of objects. Elements (counting numbers)
 et is a collection 1. Natural Numbers of the set are the individual objects, of Numbers is an
                                                                              Sets e.g., e.g., if x
  A Set is a collection of objects. Elements of the set are the individual objects, if x is an
                       {1, 2,write x ∈ S . Sets A Set is a collection of objects. Elements of the set are the individual
                             3, . . .} (N)
ment of a set a set S then we write x ∈ S . Setsdescribed by listing their their members within
  element of S then we                             are are described by listing members within
                    }. }. Use dots,. ., 1, indicate a a a S then we write x ∈ . are
  a of braces, { 2. Whole Numbers. {0,to 2, to indicate setcontinuing pattern if SareSets too
                                                   element
air pair of braces, { Use threethree dots,. . ., 3, . . .} of continuing pattern if theretheretoo are described by listing
  y members to list. list.                1. Natural Numbers (counting numbers) . ., to indicate a continuing p
                                                   a pair of braces, { }. Use three dots,.
  many members to
                                              {1, 2, 0, . 2, . .} (Z)
                    3. Integers {. . . , −3, −2, −1,3, .1,.} 3, .(N) to list.
                                                   many members
                                              of Numbers
                                        SetsSets of Numbers
                                                 x
                    4. Rational NumbersWhole Numbers0{0, 1,(Q)3, . . .}
                                          2.        : x, y ∈ Z y =         2,           Sets of Numbers
                                              y
                                              3. Integers {. . .          −2,
. Natural Numbers (counting numbers) numbers , −3,have −1, 0, 1, 2, 3, . . .} (Z)
                      Numbers (counting numbers)
     1. Natural 5. Irrational Numbers are                            that     non-
                                                            1.
   {1, 2,{1,.2,.} . . .} repeating and non-terminating Natural Numbers (counting numbers)
          3, . 3, (N) (N)                                       decimal expansion.
                                           √ 4. Rational {1, 2, 3, . .} x :
                         Examples are 2, base for natural log .e ≈ y(N)x, y ∈ Z y = 0
                                                                 Numbers 2.7,                           (Q)
. Whole Numbers {0, 1,{0,3, .2,.} . . .}
     2. Whole Numbers               2, 1, . 3,
                         π ≈ 3.14. (I)
                                                            2. Whole Numbers {0, 1, 2, 3, . . .}
                     ,{. . . ,−2, −1, 0, 1, 2,5. .2,.} . of.} Numbers irra-
. Integers {. . . 6. Real Numbers0,3, Irrational rational and are numbers that have non-
     3. Integers       −3, −3, −2, −1, 1, . 3, . (Z) (Z)
                                               consist       all
                                                            3. and non-terminating decimal expansion.
                                                  repeating Integers {. . . , −3, −2, −1, 0, 1, 2, 3, . . .} (Z)
                                                                      √
                         tional numbers. (R)
                                  x x             Examples are 2, base for natural log e ≈ 2.7,
     4. Rational Numbers : x, y: ∈ Zπy≈Z3.14. 0(Q) (Q)
. Rational Numbers                            x, y ∈= 0 = (I)
                                                         y
                                  y     y              Relationship among Sets x : x, y ∈ Z y = 0
                                                            4. Rational Numbers                                  (Q)
                                                                                         y
     5. Irrational Numbers B numbers have non-
                 Numbers and are 6. that Numbers consist of all rational and irra-
. Irrational Given sets Aare numbers Realthat have non-
                                                            5. Irrational
   repeating and non-terminating decimal expansion. A(R) Numbers are numbers that have non-
                                       A ⊂ B every numbers.
         repeating √ non-terminating tional element of is an element of B
                       and
                  Subset √                         decimal expansion.
         Examples 2, 2, forA ∪ B natural e consisting of and element of A and decimal expansion.
   Examples are are base base naturalthe setlog repeatingevery non-terminating every element of B
                  Union                   for       log ≈ e2.7, 2.7,
                                                                   ≈            √
   π ≈ 3.14. 3.14. (I)
         π≈      (I)                                            Examples are Relationship among Sets≈ 2.7,
                                                                                  2, base for natural log e
                  Interesection        A ∩ B the set of all≈ 3.14. in both A and B
                                                                π  elements (I)
     6. Numbers
. RealReal Numbers                     ∅ of all sets and irra-
                  empty consist of all rational A and Bno elements
                             set consistGiven set containing irra-
                                                    rational and
   tional numbers. sets A and B we have
         tional numbers.   (R) (R)                          6. Real Numbers consist of all rational and irra-
                 Given
                                           Subset                 A ⊂ B every (R)
                                                                tional numbers. element of A is an element of B
                                     Relationship among SetsSets
                                           Relationship among
                                           Union                  A ∪ B the set consisting of every element of A and every el
                                                                                           Relationship among Sets
en sets A and B B                          Interesection          A ∩ B the set of all elements in both A and B
  Given sets A and
                                           empty set                         B
                                                       Given sets A andset containing no elements
                                                                  ∅
bset
   Subset        A ⊂ A ⊂ every element of A of anis an element of B
                         B B every element is A element of B
 ion
   Union         A ∪ B ∪ B set consisting of Subsetelement ofA ⊂ B every element ofof A is an element of B
                                                         every                A and every element B
                         A the the set consisting of every element of A and every element of B
                 A A the the set elements in both A andAand
                                                         Union                 ∪ B the set consisting of every element of A an
   Interesection ∩ B ∩ B set of allof all elements in both A B B
 eresection
 pty set set ∅                                           Interesection      A ∩ B the set of all elements in both A and B
   empty                 ∅ set containing no elements
                                     set containing no elements
                                                         empty set          ∅         set containing no elements
               If A and B have no elements in common we write A ∩ B = ∅ and we say that A and B are
               disjoint.

				
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