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INSTRUCTIONS: Select the correct translation for each problem.
1. Redbook increases circulation or both Glamour hires models and Cosmo raises its price.
a. R ∨ G • C
b. R ⊃ (G • C)
c. R • (G ∨ C)
d. (G • C) ⊃ R
e. R ∨ (G • C)
2. If Shape expands coverage, then neither Money hires new writers nor Forbes solicits new advertisers.
a. S ⊃ (∼M ∨ F)
b. S ⊃ ∼(M ∨ F)
c. S ⊃ (∼M ∨ ∼F)
d. S ⊃ ∼(M • F)
e. ∼(M ∨ F) ⊃ S
3. People raises its price only if either Shape expands coverage or Health does not increase circulation.
a. P ⊃ S ∨ ∼H
b. (P ⊃ S) ∨ ∼H
c. (S ∨ ∼H) ⊃ P
d. P ⊃ (S ∨ ∼H)
e. P ≡ (S ∨ ∼H)
4. Not both Playboy changes its image and Maxim changes its cover given that Glamour hires models.
a. G ⊃ ∼(P • M)
b. ∼(P • M) ≡ G
c. ∼(P • M) ⊃ G
d. ∼(P • M) ∨ G
e. G ⊃ (∼P • ∼M)
5. Forbes increases circulation if and only if both Shape and Health do not raise their price.
a. F ≡ (∼S ∨ ∼H)
b. F ⊃ (∼S • ∼H)
c. F ≡ (∼S • ∼H)
d. F ≡ ∼(S • H)
e. (∼S • ∼H) ⊃ F
6. If Redbook‘s hiring models implies that Cosmo changes its cover, then either Maxim becomes more risqué or Playboy
deletes its centerfold.
a. R ⊃ [C ⊃ (M ∨ P)]
b. (R ⊃ C) ≡ (M ∨ P)
c. (C ⊃ R) ⊃ (M ∨ P)
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d. (R ⊃ C) ⊃ (M ∨ P)
e. (M ∨ P) ⊃ (R ⊃ C)
7. If Forbes increases circulation, then if both Health raises its price and Shape expands coverage, then Money solicits
new advertisers.
a. F ⊃ [(H • S) ⊃ M]
b. (H • S) ⊃ (F ⊃ M)
c. F ⊃ (H • S) ⊃ M
d. [F ⊃ (H • S)] ⊃ M
e. (F ⊃ H) • (S ⊃ M)
8. Glamour‘s hiring models is a sufficient condition for Cosmo‘s adding new features unless Playboy‘s deleting its
centerfold is a necessary condition for Maxim‘s changing its image.
a. (C ⊃ G) ⊃ (P ⊃ M)
b. G ⊃ [C ∨ (P ⊃ M)]
c. (C ⊃ G) ∨ (P ⊃ M)
d. (G ⊃ C) ⊃ (M ⊃ P)
e. (G ⊃ C) ∨ (M ⊃ P)
9. Redbook‘s increasing its price is a sufficient and necessary condition for People‘s hiring new writers, provided that
Health‘s expanding coverage implies that Shape changes its cover.
a. R ≡ [P ⊃ (H ⊃S)]
b. (H ⊃ S) ⊃ (R ≡ P)
c. (R ≡ P) ⊃ (H ⊃ S)
d. (H ⊃ S) ⊃ (R ⊃ P)]
e. R ≡ [(H ⊃ S) ⊃ P]
10. Cosmo raises its price if and only if both Redbook increases circulation and Glamour hires new writers, but either
Shape or Health expands coverage if Forbes adds new features.
a. [(C ≡ R) • G] • [(F ⊃ S) ∨ H]
b. (R • G) ≡ [(C ⊃ F) ⊃ (S ∨ H)]
c. [C ≡ (R • G)] • [F ⊃ (S ∨ H)]
d. [C ⊃ (R • G)] • [F ≡ (S ∨ H)]
e. C ≡ {(R • G) • [F ⊃ (S ∨ H)]}
Proposition 1E
Given the following proposition:
∼{[(Y ≡ ∼ A) ⊃ (∼ X ∨ Y)] • (∼ B ∨ ∼ X)}
11. Given that A and B are true and X and Y are false, determine the truth value of Proposition 1E.
a. True.
b. False.
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12. In Proposition 1E, the main operator is a:
a. Dot.
b. Triple bar.
c. Wedge.
d. Tilde.
e. Horseshoe.
Proposition 2E
Given the following proposition:
[∼ (A ∨ Y) ≡ (∼ X ⊃ B)] ∨ [∼ (Y • ∼ B) ⊃ (X ⊃ ∼ A)]
13. Given that A and B are true and X and Y are false, determine the truth value of Proposition 2E.
a. True.
b. False.
14. In Proposition 2E, the main operator is a:
a. Horseshoe.
b. Dot.
c. Tilde.
d. Triple bar.
e. Wedge.
INSTRUCTIONS: Use an ordinary truth table to answer the following problems. Construct the truth table as per the
instructions in the textbook.
Statement 1E
Given the following statement:
(G ≡ ∼ H) ∨ (H ⊃ G)
15. Statement 1E is:
a. Logically equivalent.
b. Self-contradictory.
c. Tautologous.
d. Contingent.
e. Consistent.
16. The truth table for Statement 1E has how many lines?
a. Six.
b. Eight.
c. Two.
d. Four.
e. Nine.
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21. Given the pair of statements:
I ≡ C and C • ∼ I
These statements are:
a. Valid.
b. Consistent.
c. Logically equivalent.
d. Contradictory.
e. Inconsistent.
22. Given the pair of statements:
W ⊃ (J • ∼ M) and (J ∨ ∼ W) • ∼ (M • W)
These statements are:
a. Inconsistent.
b. Logically equivalent.
c. Contradictory.
d. Valid.
e. Consistent.
23. Given the argument:
S ∨ L / L ⊃ ∼ S // S ∨ ∼ L
This argument is:
a. Invalid; fails in 1st line.
b. Invalid; fails in 2nd line.
c. Valid.
d. Invalid; fails in 3rd line.
e. Invalid; fails in 4th line.
24. Given the argument:
N ≡ D / D ⊃ ∼ N // ∼ N
This argument is:
a. Invalid; fails in 2nd line.
b. Invalid; fails in 4th line.
c. Valid.
d. Invalid; fails in 5th line.
INSTRUCTIONS: Use indirect truth tables to answer the following problems.
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25. Given the argument:
H ⊃ (R • J) / (R ∨ A) ⊃ E / J ⊃ ∼ P / E ⊃ P // ∼ H
This argument is:
a. Valid.
b. Invalid.
c. Uncogent.
d. Cogent.
e. Sound.
26. Given the argument:
Q ⊃ (C • N) / S ⊃ (C ∨ N) / Q ∨ S / N ⊃ K // K • C
This argument is:
a. Sound.
b. Uncogent.
c. Invalid.
d. Cogent.
e. Valid.
27. Given the statements:
G • W / G ⊃ (∼ R ⊃ Q) / W ⊃ (R ⊃ ∼ Q) / G ⊃ Q
These statements are:
a. Inconsistent.
b. Logically equivalent.
c. Invalid.
d. Tautologous.
e. Consistent.
28. Given the statements:
(E ∨ P) ⊃ H / ∼ N ⊃ (P • E) / N ⊃ ∼ H / E ≡ ∼ P
These statements are:
a. Contradictory.
b. Tautologous.
c. Valid.
d. Inconsistent.
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. ∼G ⊃ E
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E ⊃ ∼J
∼G ⊃ ∼J
a. MP—valid.
b. HS—valid.
c. Invalid.
d. CD—valid.
e. DS—valid.
30. (J ⊃ ∼M) • (∼A ⊃ R)
M ∨ ∼R
∼J ∨ A
a. DD—valid.
b. Invalid.
c. CD—valid.
d. MT—valid.
e. CD—invalid.
31. W
∼W ⊃ ∼K
K
a. AC—invalid.
b. MT—valid.
c. DA—invalid.
d. DS—invalid.
e. MP—valid.
32. P ∨ ∼D
∼P
∼D
a. MP—valid.
b. HS—valid.
c. MT—valid.
d. DA—invalid.
e. DS—valid.
33. ∼A
∼A ∨ J
J
a. AC—invalid.
b. DS—invalid.
c. MP—valid.
d. Invalid.
e. HS—valid.
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34. S ⊃ ∼M
S
∼M
a. HS—valid.
b. AC—invalid.
c. MT—valid.
d. DS—valid.
e. MP—valid.
35. S ⊃ ∼R
∼R
S
a. MT—invalid.
b. MP—valid.
c. DA—invalid.
d. AC—invalid.
e. DS—valid.
36. ∼B ⊃ K
∼W ⊃ ∼B
W ⊃ ∼K
a. DD—invalid.
b. Invalid.
c. HS—valid.
d. CD—valid.
e. DS—valid.
37. (B ⊃ ∼T) • (∼B ⊃ N)
∼B ∨ B
∼T ∨ N
a. CD—valid.
b. Invalid.
c. DD—valid.
d. DA—invalid.
e. MP—valid.
38. ∼F
∼B ⊃ F
B
a. MP—valid.
b. DS—invalid.
c. MT—valid.
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d. DA—invalid.
e. DS—valid.