76 CHAPTER 2 Sets *See Instructor Answer Appendix Exercises Warm Up Exercises In Exercises 1– 4, fill in the blank with an appropriate word, phrase, or symbol(s). 1. The number of regions created when constructing a Venn diagram with three overlapping sets is ____________. 8 2. a) When constructing a Venn diagram with three overlapping sets, region ____________ is generally completed first. V b) When constructing a Venn diagram with three overlapping sets, after completing region V, the next regions generally completed are II, IV, and ____________. VI 3. Complete De Morgan’s laws: a) <A B ( )′ =____________ > A B ′ ′ b) >A B ( )′ =____________ < A B ′ ′ 4. When using Venn diagrams to verify or determine whether set statements are equal we use ____________ reasoning. Deductive Practice the Skills 5. Construct a Venn diagram illustrating the following sets. * = = = = U abcdef ghij A a b c d e B d e f g h C a c e g i {,,, ,,,,,,} {, , , , } {, , , , } {,,,,} 6. Construct a Venn diagram illustrating the following sets. * U A B C {1, 2, 3, 4, 5, 6, 7, 8, 9} {1, 2, 3, 4} {3, 4, 6, 7, 9} {2, 4, 6, 8} = = = = 7. Construct a Venn diagram illustrating the following sets. * U A B C {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} {2, 3, 4, 7, 8} {l, 2, 3, 6, 8} {2, 4, 5, 6, 8, 10} = = = = 8. Construct a Venn diagram illustrating the following sets. * U abcdef ghij A c d e g h i B a c d g C c f i j {,,, ,,,,,,} {, , , , , } {, , , } {, , , } = = = = 9. Rock Bands Construct a Venn diagram illustrating the following sets. * = = = = U A B C {Blackpink, Evanescence, Funkadelic, Hoobastank, Jaguares, Loudness, Outkast, Radiohead, Santana, War} {Blackpink, Jaguares, Loudness, Radiohead, Santana} {Funkadelic, Outkast, Radiohead, War} {Blackpink, Hoobestank, Radiohead, Santana, War} 10. Broadway Musicals Construct a Venn diagram illustrating the following sets. * U A B C {Aladdin, Cats, Dreamgirls, Evita, Grease, Hamilton, Newsies, Oliver, Rent, Wicked} {Dreamgirls, Evita, Grease, Wicked} {Aladdin, Grease, Hamilton, Oliver, Newsies} {Cats, Grease, Hamilton, Newsies, Wicked} = = = = 11. Cars Construct a Venn diagram illustrating the following sets. * U A B C {Audi, Chevrolet, Dodge, Ford, Honda, Kia, Nissan, Subaru, Toyota, Volkswagen} {Ford, Honda, Kia, Nissan, Subaru} {Honda, Nissan, Subaru, Toyota} {Chevrolet, Nissan, Subaru, Toyota} = = = = 12. Jazz Musicians Construct a Venn diagram illustrating the following sets. Use the musicians’ last names in the Venn diagram. * U A B C {Louis Armstrong, Glenn Miller, Stan Kenton, Charlie Parker, Duke Ellington, Benny Goodman, Count Basie, John Coltrane, Dizzy Gillespie, Miles Davis, Thelonius Monk} {Stan Kenton, Count Basie, Dizzy Gillespie, Duke Ellington, Thelonius Monk} {Louis Armstrong, Glenn Miller, Count Basie, Duke Ellington, Miles Davis} {Count Basie, Miles Davis, Stan Kenton, Charlie Parker, Duke Ellington} = = = = Problem Solving In Exercises 13–24, use the Venn diagram in Fig. 2.21 to list the sets in roster form. m Blackpink SECTION 2.4 U A 1 10 3 4 5 11 2 13 C 8 6 12 14 7 B 9 Figure 2.21 Imaginechina/Imaginechina Limited/Alamy Stock Photo
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