INSTRUCTIONS: Select the Correct Translation for Each Problem

Chapter 6 -1

MULTIPLE CHOICE

INSTRUCTIONS: Select the correct translation for each problem.

1.Princess drops its dress codes or Oceania enlarges its fleet, and Seabourn reduces its fares.

a. / P  (O  S)
b. / (P  O)  S
c. / P  (O  S)
d. / P  O  S
e. / (P  O)  S

ANS:E

2.Not either Regent enlarges its casinos or Celebrity revises its itineraries if Holland remodels its staterooms.

a. / H (R  C)
b. / H  (R  C)
c. / (R  C)  H
d. / (R C)  H
e. / H  (R C)

ANS:A

3.Norwegian improves its entertainment only if both Disney does not promote family cruises and Windstar does not diversify its activities.

a. / N  (D W)
b. / N  (D W)
c. / (D W)  N
d. / N (D  W)
e. / (D  W)  N

ANS:B

4.Either Azmara or Seabourn do not open new boutiques provided that Princess improves its cuisine.

a. / P  (A S)
b. / (A S)  P
c. / (A S)  P
d. / P (A  S)
e. / (A  S)  P

ANS:A

5.Carnival advertises its parties if and only if Disney's promoting family cruises implies that Norwegian improves its entertainment.

a. / (C  D)  N
b. / (C  D)  (N  C)
c. / C  (D  N)
d. / C  (D  N)
e. / C  (N  D)

ANS:C

6.If Disney promotes family cruises, then if either Holland remodels its staterooms or Regent enlarges its casinos, then Windstar diversifies its activities.

a. / [D  (H  R)]  W
b. / D  [(H  R)  W]
c. / [(H  R)  D]  W
d. / D  [(H  R)  W]
e. / D  (H  R)  W

ANS:D

7.Princess and Azmara improve gym facilities only if neither Carnival controls rowdiness nor Seabourn reduces fares.

a. / (P  A)  (C  S)
b. / (P  A) (C  S)
c. / (C  S)  (P  A)
d. / (P  A)  (C S)
e. / (C S)  (P  A)

ANS:B

8.Regent's enlarging its casinos is a necessary condition for Disney's offering games if and only if Windstar's diversifying its activities is a sufficient condition for Costa's enlarging its nightspots.

a. / (R  D)  (C  W)
b. / (D  W)  (R  C)
c. / (D  R)  (W  C)
d. / (D  R)  (W  C)
e. / (R  D)  (W  C)

ANS:C

9.Azmara's opening new boutiques is a sufficient and necessary condition for both Norwegian's improving entertainment and Holland's remodeling its staterooms if Princess's dropping its dress codes implies that Celebrity revises its itineraries.

a. / (P  C)  [(A  N)  (A  C)]
b. / (P  C)  [A  (N  H)]
c. / [A  (N  H)]  (P  C)
d. / [(A  N)  (A  C)]  (P  C)
e. / (P  C)  [A  (N  H)]

ANS:E

10.Seabourn revises its menu given that Norwegian and Princess halt tipping, unless Oceania enlarges its fleet if and only if both Costa improves its gym facilities and Regent enlarges its casinos.

a. / [S  (N  P)]  [O  (C  R)]
b. / [(N  P)  S]  [O  (C  R)]
c. / [(N  P)  S]  [O  (C  R)]
d. / [S  (N  P)]  [O  (C  R)]
e. / [S  (N  P)]  [O  (C  R)]

ANS:C

Proposition 1B

Given the following proposition:

[(A  B)  X]  [Y  (A  X)]

11.Given that A and B are true and X and Y are false, determine the truth value of Proposition 1B.

a. / True.
b. / False.

ANS:B

12.In Proposition 1B, the main operator is a:

a. / Dot.
b. / Triple bar.
c. / Wedge.
d. / Tilde.
e. / Horseshoe.

ANS:E

Proposition 2B

Given the following proposition:

[(A  Y)  (B X)] [(B X)  (Y  A)]

13.Given that A and B are true and X and Y are false, determine the truth value of Proposition 2B.

a. / True.
b. / False.

ANS:A

14.In Proposition 2B, the main operator is a:

a. / Horseshoe.
b. / Dot.
c. / Tilde.
d. / Wedge.
e. / Triple bar.

ANS:D

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.

29.D C

R D

R C

a. / MPvalid.
b. / DSvalid.
c. / Invalid.
d. / CDvalid.
e. / HSvalid.

ANS:E

30.(C J)  (P  L)

J L

C P

a. / CDvalid.
b. / Invalid.
c. / DDvalid.
d. / MTvalid.
e. / CDinvalid.

ANS:C

31.M

M G

G

a. / ACinvalid.
b. / MTvalid.
c. / DSinvalid.
d. / DAinvalid.
e. / MPvalid.

ANS:D

32.N  A

N

A

a. / DSvalid.
b. / HSvalid.
c. / MTvalid.
d. / DAinvalid.
e. / MPvalid.

ANS:A

33.D E

E

D

a. / ACinvalid.
b. / DSinvalid.
c. / Invalid.
d. / MPvalid.
e. / HSvalid.

ANS:C

34.K N

K

N

a. / HSvalid.
b. / MPvalid.
c. / MTvalid.
d. / DSvalid.
e. / ACinvalid.

ANS:B

35.Q

H Q

H

a. / MTinvalid.
b. / MPvalid.
c. / DAinvalid.
d. / DSvalid.
e. / ACinvalid.

ANS:E

36.E A

B E

B  A

a. / Invalid.
b. / DDinvalid.
c. / HSvalid.
d. / CDvalid.
e. / DSvalid.

ANS:A

37.(H  K)  (H T)

H H

T  K

a. / Invalid.
b. / CDvalid.
c. / DDvalid.
d. / DAinvalid.
e. / MPvalid.

ANS:B

38.S F

F

S

a. / MPvalid.
b. / DSinvalid.
c. / DAinvalid.
d. / MTvalid.
e. / DSvalid.

ANS:D