{"id":214,"date":"2023-02-01T00:03:37","date_gmt":"2023-02-01T00:03:37","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/chapter\/assignment-set-theory-problem-set\/"},"modified":"2023-02-01T00:03:37","modified_gmt":"2023-02-01T00:03:37","slug":"assignment-set-theory-problem-set","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/chapter\/assignment-set-theory-problem-set\/","title":{"raw":"Assignment: Set Theory Problem Set","rendered":"Assignment: Set Theory Problem Set"},"content":{"raw":"\n
    \n \t
  1. List out the elements of the set \u201cThe letters of the word Mississippi\u201d<\/li>\n \t
  2. List out the elements of the set \u201cMonths of the year\u201d<\/li>\n \t
  3. Write a verbal description of the set {3, 6, 9}<\/li>\n \t
  4. Write a verbal description of the set {a, i, e, o, u}<\/li>\n \t
  5. Is {1, 3, 5} a subset of the set of odd integers?<\/li>\n \t
  6. Is {A, B, C} a subset of the set of letters of the alphabet?<\/li>\n<\/ol>\nFor problems 7-12, consider the sets below, and indicate if each statement is true or false.\n\nA = {1, 2, 3, 4, 5}   B = {1, 3, 5}     C = {4, 6}     U = {numbers from 0 to 10}\n
      \n \t
    1. 3 \u220a B<\/em><\/li>\n \t
    2. 5 \u220a C <\/em><\/li>\n \t
    3. B<\/em> \u2282 A<\/em><\/li>\n \t
    4. C<\/em> \u2282 A<\/em><\/li>\n \t
    5. C<\/em> \u2282 B<\/em><\/li>\n \t
    6. C<\/em> \u2282 U<\/i><\/li>\n<\/ol>\nUsing the sets from above, and treating U<\/em> as the Universal set, find each of the following:\n
        \n \t
      1. A <\/em>\u22c3 B<\/em><\/li>\n \t
      2. A <\/em>\u22c3 C<\/em><\/li>\n \t
      3. A <\/em>\u22c2 C <\/em><\/li>\n \t
      4. B <\/em>\u22c2 C<\/em><\/li>\n \t
      5. A c<\/sup><\/em><\/li>\n \t
      6. B c<\/sup><\/em><\/li>\n<\/ol>\nLet D = {b, a, c, k},   E = {t, a, s, k},   F = {b, a, t, h}. Using these sets, find the following:\n
          \n \t
        1. D c <\/sup><\/em>\u22c2 E<\/em><\/li>\n \t
        2. F c <\/sup><\/em>\u22c2 D<\/em><\/li>\n \t
        3. (D <\/em>\u22c2 E<\/em>) \u22c3 F<\/em><\/li>\n \t
        4. D <\/em>\u22c2 (E<\/em> \u22c3 F<\/em>)<\/li>\n \t
        5. (F <\/em>\u22c2 E<\/em>)c<\/em><\/sup> \u22c2 D<\/em><\/li>\n \t
        6. (D <\/em>\u22c3 E<\/em>)c<\/em><\/sup> \u22c2 F<\/em><\/li>\n<\/ol>\nCreate a Venn diagram to illustrate each of the following:\n
            \n \t
          1. (F <\/em>\u22c2 E<\/em>) \u22c3 D<\/em><\/li>\n \t
          2. (D <\/em>\u22c3 E<\/em>)c<\/em><\/sup> \u22c2 F<\/em><\/li>\n \t
          3. (F c <\/sup><\/em>\u22c2 E c <\/sup><\/em>) \u22c2 D<\/em><\/li>\n \t
          4. (D <\/em>\u22c3 E<\/em>) \u22c3 F<\/em><\/li>\n<\/ol>\nWrite an expression for the shaded region.\n
              \n \t
            1. \"abc1\"<\/li>\n \t
            2. \"abc2\"<\/li>\n \t
            3. \"abc3\"<\/li>\n \t
            4. \"abc4\"<\/li>\n<\/ol>\nLet A = {1, 2, 3, 4, 5}   B = {1, 3, 5}     C = {4, 6}. Find the cardinality of the given set.\n
                \n \t
              1. n(A<\/em>)<\/li>\n \t
              2. n(B<\/em>)<\/li>\n \t
              3. n(A <\/em>\u22c3 C<\/em>)<\/li>\n \t
              4. n(A <\/em>\u22c2 C<\/em>)<\/li>\n<\/ol>\nThe Venn diagram here shows the cardinality of each set. Use this in 37-40 to find the cardinality of given set.\n\n\"Venn<\/a>\n
                  \n \t
                1. n(A <\/em>\u22c2 C<\/em>)<\/li>\n \t
                2. n(B <\/em>\u22c3 C<\/em>)<\/li>\n \t
                3. n(A <\/em>\u22c2 B <\/em>\u22c2 C c <\/sup><\/em>)<\/li>\n \t
                4. n(A <\/em>\u22c2 Bc <\/sup><\/em>\u22c2 C<\/em>)<\/li>\n \t
                5. If n(G) = 20, n(H) = 30, n(G <\/em>\u22c2 H<\/em>) = 5, find n(G <\/em>\u22c3 H<\/em>)<\/li>\n \t
                6. If n(G) = 5, n(H) = 8, n(G <\/em>\u22c2 H<\/em>) = 4, find n(G <\/em>\u22c3 H<\/em>)<\/li>\n \t
                7. A survey was given asking whether they watch movies at home from Netflix, Redbox, or a video store. Use the results to determine how many people use Redbox.\n\n\n\n\n\n\n
                  52 only use Netflix<\/td>\n62 only use Redbox<\/td>\n<\/tr>\n
                  24 only use a video store<\/td>\n16 use only a video store and Redbox<\/td>\n<\/tr>\n
                  48 use only Netflix and Redbox<\/td>\n30 use only a video store and Netflix<\/td>\n<\/tr>\n
                  10 use all three<\/td>\n25 use none of these<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n \t
                8. A survey asked buyers whether color, size, or brand influenced their choice of cell phone. The results are below. How many people were influenced by brand?\n\n\n\n\n\n\n
                  5 only said color<\/td>\n8 only said size<\/td>\n<\/tr>\n
                  16 only said brand<\/td>\n20 said only color and size<\/td>\n<\/tr>\n
                  42 said only color and brand<\/td>\n53 said only size and brand<\/td>\n<\/tr>\n
                  102 said all three<\/td>\n20 said none of these<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n \t
                9. Use the given information to complete a Venn diagram, then determine: a) how many students have seen exactly one of these movies, and b) how many had seen only Star Wars<\/em>.\n\n\n\n\n\n\n
                  18 had seen The Matrix <\/em>(M<\/em>)<\/td>\n24 had seen Star Wars (SW)<\/em><\/td>\n<\/tr>\n
                  20 had seen Lord of the Rings (LotR)<\/em><\/td>\n <\/em>10 had seen M<\/em> and SW<\/em><\/td>\n<\/tr>\n
                  14 had seen LotR<\/em> and SW<\/em><\/td>\n12 had seen M<\/em> and LotR<\/em><\/td>\n<\/tr>\n
                  6 had seen all three<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n \t
                10. A survey asked people what alternative transportation modes they use. Using the data to complete a Venn diagram, then determine: a) what percent of people only ride the bus, and b) how many people don\u2019t use any alternate transportation.\n\n\n\n\n\n\n
                  25% walk<\/td>\n10% ride a bicycle and walk<\/td>\n<\/tr>\n
                  30% use the bus<\/td>\n20% ride a bicycle<\/td>\n<\/tr>\n
                  5% use the bus and ride a bicycle<\/td>\n12% use the bus and walk<\/td>\n<\/tr>\n
                  2% use all three<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<\/ol>\n","rendered":"
                    \n
                  1. List out the elements of the set \u201cThe letters of the word Mississippi\u201d<\/li>\n
                  2. List out the elements of the set \u201cMonths of the year\u201d<\/li>\n
                  3. Write a verbal description of the set {3, 6, 9}<\/li>\n
                  4. Write a verbal description of the set {a, i, e, o, u}<\/li>\n
                  5. Is {1, 3, 5} a subset of the set of odd integers?<\/li>\n
                  6. Is {A, B, C} a subset of the set of letters of the alphabet?<\/li>\n<\/ol>\n

                    For problems 7-12, consider the sets below, and indicate if each statement is true or false.<\/p>\n

                    A = {1, 2, 3, 4, 5}   B = {1, 3, 5}     C = {4, 6}     U = {numbers from 0 to 10}<\/p>\n

                      \n
                    1. 3 \u220a B<\/em><\/li>\n
                    2. 5 \u220a C <\/em><\/li>\n
                    3. B<\/em> \u2282 A<\/em><\/li>\n
                    4. C<\/em> \u2282 A<\/em><\/li>\n
                    5. C<\/em> \u2282 B<\/em><\/li>\n
                    6. C<\/em> \u2282 U<\/i><\/li>\n<\/ol>\n

                      Using the sets from above, and treating U<\/em> as the Universal set, find each of the following:<\/p>\n

                        \n
                      1. A <\/em>\u22c3 B<\/em><\/li>\n
                      2. A <\/em>\u22c3 C<\/em><\/li>\n
                      3. A <\/em>\u22c2 C <\/em><\/li>\n
                      4. B <\/em>\u22c2 C<\/em><\/li>\n
                      5. A c<\/sup><\/em><\/li>\n
                      6. B c<\/sup><\/em><\/li>\n<\/ol>\n

                        Let D = {b, a, c, k},   E = {t, a, s, k},   F = {b, a, t, h}. Using these sets, find the following:<\/p>\n

                          \n
                        1. D c <\/sup><\/em>\u22c2 E<\/em><\/li>\n
                        2. F c <\/sup><\/em>\u22c2 D<\/em><\/li>\n
                        3. (D <\/em>\u22c2 E<\/em>) \u22c3 F<\/em><\/li>\n
                        4. D <\/em>\u22c2 (E<\/em> \u22c3 F<\/em>)<\/li>\n
                        5. (F <\/em>\u22c2 E<\/em>)c<\/em><\/sup> \u22c2 D<\/em><\/li>\n
                        6. (D <\/em>\u22c3 E<\/em>)c<\/em><\/sup> \u22c2 F<\/em><\/li>\n<\/ol>\n

                          Create a Venn diagram to illustrate each of the following:<\/p>\n

                            \n
                          1. (F <\/em>\u22c2 E<\/em>) \u22c3 D<\/em><\/li>\n
                          2. (D <\/em>\u22c3 E<\/em>)c<\/em><\/sup> \u22c2 F<\/em><\/li>\n
                          3. (F c <\/sup><\/em>\u22c2 E c <\/sup><\/em>) \u22c2 D<\/em><\/li>\n
                          4. (D <\/em>\u22c3 E<\/em>) \u22c3 F<\/em><\/li>\n<\/ol>\n

                            Write an expression for the shaded region.<\/p>\n

                              \n
                            1. \"abc1\"<\/li>\n
                            2. \"abc2\"<\/li>\n
                            3. \"abc3\"<\/li>\n
                            4. \"abc4\"<\/li>\n<\/ol>\n

                              Let A = {1, 2, 3, 4, 5}   B = {1, 3, 5}     C = {4, 6}. Find the cardinality of the given set.<\/p>\n

                                \n
                              1. n(A<\/em>)<\/li>\n
                              2. n(B<\/em>)<\/li>\n
                              3. n(A <\/em>\u22c3 C<\/em>)<\/li>\n
                              4. n(A <\/em>\u22c2 C<\/em>)<\/li>\n<\/ol>\n

                                The Venn diagram here shows the cardinality of each set. Use this in 37-40 to find the cardinality of given set.<\/p>\n

                                \"Venn<\/a><\/p>\n

                                  \n
                                1. n(A <\/em>\u22c2 C<\/em>)<\/li>\n
                                2. n(B <\/em>\u22c3 C<\/em>)<\/li>\n
                                3. n(A <\/em>\u22c2 B <\/em>\u22c2 C c <\/sup><\/em>)<\/li>\n
                                4. n(A <\/em>\u22c2 Bc <\/sup><\/em>\u22c2 C<\/em>)<\/li>\n
                                5. If n(G) = 20, n(H) = 30, n(G <\/em>\u22c2 H<\/em>) = 5, find n(G <\/em>\u22c3 H<\/em>)<\/li>\n
                                6. If n(G) = 5, n(H) = 8, n(G <\/em>\u22c2 H<\/em>) = 4, find n(G <\/em>\u22c3 H<\/em>)<\/li>\n
                                7. A survey was given asking whether they watch movies at home from Netflix, Redbox, or a video store. Use the results to determine how many people use Redbox.
                                  \n\n\n\n\n\n\n
                                  52 only use Netflix<\/td>\n62 only use Redbox<\/td>\n<\/tr>\n
                                  24 only use a video store<\/td>\n16 use only a video store and Redbox<\/td>\n<\/tr>\n
                                  48 use only Netflix and Redbox<\/td>\n30 use only a video store and Netflix<\/td>\n<\/tr>\n
                                  10 use all three<\/td>\n25 use none of these<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n
                                8. A survey asked buyers whether color, size, or brand influenced their choice of cell phone. The results are below. How many people were influenced by brand?
                                  \n\n\n\n\n\n\n
                                  5 only said color<\/td>\n8 only said size<\/td>\n<\/tr>\n
                                  16 only said brand<\/td>\n20 said only color and size<\/td>\n<\/tr>\n
                                  42 said only color and brand<\/td>\n53 said only size and brand<\/td>\n<\/tr>\n
                                  102 said all three<\/td>\n20 said none of these<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n
                                9. Use the given information to complete a Venn diagram, then determine: a) how many students have seen exactly one of these movies, and b) how many had seen only Star Wars<\/em>.
                                  \n\n\n\n\n\n\n
                                  18 had seen The Matrix <\/em>(M<\/em>)<\/td>\n24 had seen Star Wars (SW)<\/em><\/td>\n<\/tr>\n
                                  20 had seen Lord of the Rings (LotR)<\/em><\/td>\n <\/em>10 had seen M<\/em> and SW<\/em><\/td>\n<\/tr>\n
                                  14 had seen LotR<\/em> and SW<\/em><\/td>\n12 had seen M<\/em> and LotR<\/em><\/td>\n<\/tr>\n
                                  6 had seen all three<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n
                                10. A survey asked people what alternative transportation modes they use. Using the data to complete a Venn diagram, then determine: a) what percent of people only ride the bus, and b) how many people don\u2019t use any alternate transportation.
                                  \n\n\n\n\n\n\n
                                  25% walk<\/td>\n10% ride a bicycle and walk<\/td>\n<\/tr>\n
                                  30% use the bus<\/td>\n20% ride a bicycle<\/td>\n<\/tr>\n
                                  5% use the bus and ride a bicycle<\/td>\n12% use the bus and walk<\/td>\n<\/tr>\n
                                  2% use all three<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<\/ol>\n\n\t\t\t
                                  \n\t\t\t

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