<p>Chapter 6 Test C</p><p>MULTIPLE CHOICE</p><p>INSTRUCTIONS: Select the correct translation for each problem. Use capital letters to represent affirmative English statements.</p><p>1. Coors is smooth or both Beck's is subtle and Guinness is heavy. a. C  (B  G) b. C  (B  G) c. (C  B)  G d. (C  B)  G e. C  B  G ANS: A PTS: 2</p><p>2. Budweiser is bland if either Heineken is balanced or Foster's is refreshing. a. (H  B)  F b. (B  H)  F c. B  (H  F) d. B  H  F e. (H  F)  B ANS: E PTS: 2</p><p>3. Alaskan is sweet only if neither Heineken is balanced nor Pabst is clean tasting. a. A  (H  P) b. A  H  P c. (H  P)  A d. A  (H  P) e. (H  P)  A ANS: D PTS: 2</p><p>4. Sierra is hearty given that Michelob's being flavorful implies that Guinness is heavy. a. (S  M)  G b. (G  M)  S c. S  (M  G) d. M  (G  S) e. (M  G)  S ANS: E PTS: 2</p><p>5. Harp is soothing if and only if both Miller is not zesty and Coors is not smooth. a. H  (M  C) b. (H  M)  (H  C) c. H  (M  C) d. (H  M)  (H  C) e. H  (M  C) ANS: C PTS: 2 6. Sierra is hearty only if Budweiser is bland, given that both Heineken is balanced and Michelob is complex. a. (S  B)  (H  M) b. (H  M)  (S  B) c. (H  M)  (B  S) d. (S  B)  (H  M) e. (H  M)  (S  B) ANS: B PTS: 2</p><p>7. Corona is drinkable if Pabst is clean tasting, and Foster's is refreshing only if Guinness is dark. a. (P  C)  (F  G) b. (C  P)  (F  G) c. (C  P)  (G  F) d. (P  F)  (C  G) e. (P  C)  (F  G) ANS: A PTS: 2</p><p>8. Michelob's being complex is a necessary condition for Heineken's being balanced unless Alaskan's being sweet is a sufficient condition for Carlsberg's being malty. a. (M  H)  (A  C) b. (M  H)  (A  C) c. (M  H)  (C  A) d. (H  M)  (A  C) e. (H  M)  (A  C) ANS: D PTS: 2</p><p>9. If Heineken's being balanced implies that either Sierra is hearty or Alaskan is not sweet, then Miller's being zesty is a sufficient and necessary condition for Coors's being smooth. a. [H  (S  A)]  (M  C) b. [H  (S  A)]  (M  C) c. [H  (S  A)]  (M  C) d. H  [(S  A)  (M  C)] e. H  [(S  A)  (M  C)] ANS: B PTS: 2</p><p>10. Sierra's being hearty is a necessary condition for both Coors's being smooth and Harp's being crisp; moreover, Guinness is dark if and only if Alaskan's being sweet implies that Beck's is subtle. a. [S  (C  H)]  [G  (B  A)] b. [S  (C  H)]  [G  (A  B)] c. [(C  H)  S]  [G  (A  B)] d. [(C  H)  S]  [G  (A  B)] e. [(C  H)  S]  [G  (A  B)] ANS: C PTS: 2</p><p>Proposition 1C Given the following proposition: {[(B  X)  Y]  [X  (A  Y)]}</p><p>11. Given that A and B are true and X and Y are false, determine the truth value of Proposition 1C. a. True. b. False. ANS: A PTS: 2</p><p>12. In Proposition 1C, the main operator is a: a. Dot. b. Horseshoe. c. Wedge. d. Triple bar. e. Tilde. ANS: E PTS: 2</p><p>Proposition 2C Given the following proposition: [(A  Y)  (B  X)]  [(B  X)  (X  A)]</p><p>13. Given that A and B are true and X and Y are false, determine the truth value of Proposition 2C. a. True. b. False. ANS: B PTS: 2</p><p>14. In Proposition 2C, the main operator is a: a. Triple bar. b. Wedge. c. Tilde. d. Dot. e. Horseshoe. ANS: D PTS: 2</p><p>INSTRUCTIONS: Determine whether the following symbolized arguments are valid or invalid by identifying the form of each. In some cases the argument must be rewritten using double negation or commutativity before it has a named form. Those arguments without a specific name are invalid.</p><p>29. S  T T S a. MPvalid. b. DSvalid. c. MTvalid. d. DAinvalid. e. Invalid. ANS: B PTS: 2</p><p>30. H  B B H a. MTvalid. b. Invalid. c. MPvalid. d. DSvalid. e. DAinvalid. ANS: A PTS: 2</p><p>31. B  J  J B a. DAinvalid. b. ACinvalid. c. MPvalid. d. MTvalid. e. DSvalid. ANS: B PTS: 2</p><p>32. D  M (M  A)  (D  C) A  C a. HSvalid. b. Invalid. c. DDvalid. d. MPvalid. e. CDvalid. ANS: E PTS: 2</p><p>33. K  R E  R K  E a. HSvalid. b. CDvalid. c. Invalid. d. CDinvalid. e. DAinvalid. ANS: C PTS: 2</p><p>34. F  K  N  F N  K a. MTvalid. b. HSvalid. c. Invalid. d. DDinvalid. e. CDvalid. ANS: B PTS: 2 35. P  G (H   P)  (C   G) H  C a. CDvalid. b. Invalid. c. MTvalid. d. DDvalid. e. CDinvalid. ANS: D PTS: 2</p><p>36. G  R G R a. DSinvalid. b. MPvalid. c. MTvalid. d. DAvalid. e. HSvalid. ANS: B PTS: 2</p><p>37. E  H  H E a. Invalid b. CDvalid. c. DDvalid. d. CDinvalid. e. MPvalid. ANS: A PTS: 2</p><p>38. Q  R Q R a. ACinvalid. b. MPvalid. c. HSvalid. d. MTinvalid. e. DAinvalid. ANS: E PTS: 2</p>