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INSTRUCTIONS: Select the correct translation for each problem. Use capital letters to represent affirmative English
statements.
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
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
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
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
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)
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)
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d. (S ⊃ B) ⊃ (H ⊃ M)
e. (H ⊃ M) • (S ⊃ B)
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)
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)
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)]
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)]
Proposition 1C
Given the following proposition:
∼{[(B ≡ ∼ X) ⊃ Y] ∨ [∼ X ⊃ (A ⊃ Y)]}
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.
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12. In Proposition 1C, the main operator is a:
a. Dot.
b. Horseshoe.
c. Wedge.
d. Triple bar.
e. Tilde.
Proposition 2C
Given the following proposition:
∼[(A ≡ ∼ Y) • (B ⊃ X)] • [(B ∨ ∼ X) • (X ≡ A)]
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.
14. In Proposition 2C, the main operator is a:
a. Triple bar.
b. Wedge.
c. Tilde.
d. Dot.
e. Horseshoe.
INSTRUCTIONS: Use an ordinary truth table to answer the following problems. Construct the truth table as per the
instructions in the textbook.
Statement 1C
Given the following statement:
(H ∨ ∼ K) ≡ (K ⊃ H)
15. Statement 1C is:
a. Self-contradictory.
b. Contingent.
c. Consistent.
d. Logically equivalent.
e. Tautologous.
16. The truth table for Statement 1C has how many lines?
a. Six.
b. Eight.
c. Four.
d. Two.
e. Nine.
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INSTRUCTIONS: Use an ordinary truth table to answer the following problems. Construct the truth table as per the
instructions in the textbook.
Statement 2C
Given the following statement:
[G ⊃ (R • N)] ∨ [R ⊃ (G • N)]
17. Statement 2C is:
a. Tautologous.
b. Contingent.
c. Inconsistent.
d. Self-contradictory.
e. Consistent.
18. The truth table for Statement 2C has how many lines?
a. Eight.
b. Nine.
c. Four.
d. Six.
e. Twelve.
INSTRUCTIONS: Use an ordinary truth table to answer the following problems. Construct the truth table as per the
instructions in the textbook.
19. Given the statement:
(A ∨ ∼ S) • (S • ∼ A)
This statement is:
a. Valid.
b. Tautologous.
c. Self-contradictory.
d. Contingent.
e. Inconsistent.
20. Given the pair of statements:
∼ (H ≡ R) and ∼ (R ⊃ ∼ H)
These statements are:
a. Logically equivalent.
b. Contradictory.
c. Consistent.
d. Inconsistent.
e. Invalid.
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21. Given the pair of statements:
Q ≡ N and (N • ∼ Q) ∨ (Q • ∼ N)
These statements are:
a. Contradictory.
b. Logically equivalent.
c. Inconsistent.
d. Consistent.
e. Valid.
22. Given the pair of statements:
R ⊃ ∼ B and ∼ (B • R)
These statements are:
a. Consistent.
b. Inconsistent.
c. Valid.
d. Contradictory.
e. Logically equivalent.
23. Given the argument:
K ∨ E / E ⊃ ∼ K // K ≡ ∼ E
This argument is:
a. Invalid; fails in 2nd line.
b. Valid.
c. Invalid; fails in 1st line.
d. Invalid; fails in 4th line.
e. Invalid; fails in 3rd line.
24. Given the argument:
P ∨ J / ∼(J • ∼ P) // J ≡ ∼ P
This argument is:
a. Invalid; fails in 3rd line.
b. Invalid; fails in 2nd line.
c. Invalid; fails in 1st line.
d. Valid.
e. Invalid; fails in 4th line.
INSTRUCTIONS: Use indirect truth tables to answer the following problems.
25. Given the argument:
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C ⊃ ∼ M / I ⊃ ∼ H / (N • I) ∨ (G • C) / H ∨ M // G • M
This argument is:
a. Uncogent.
b. Cogent.
c. Sound.
d. Invalid.
e. Valid.
26. Given the argument:
W ∨ ∼ S / E ∨ ∼ A / (K ∨ L) ≡ (A • S) // L ⊃ (E • W)
This argument is:
a. Invalid.
b. Uncogent.
c. Valid.
d. Cogent.
e. Sound.
27. Given the statements:
R ⊃ (Q ∨ ∼ N) / Q ⊃ (U ⊃ ∼ B) / B ⊃ (N • U) / R • B
These statements are:
a. Inconsistent.
b. Invalid.
c. Consistent.
d. Logically equivalent.
e. Tautologous.
28. Given the statements:
P ≡ (S ∨ ∼ A) / A ⊃ (M • J) / J ⊃ (P • S) / J ≡ A
These statements are:
a. Valid.
b. Contradictory.
c. Tautologous.
d. Inconsistent.
e. Consistent.
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. ∼S ∨ ∼T
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T
∼S
a. MP—valid.
b. DS—valid.
c. MT—valid.
d. DA—invalid.
e. Invalid.
30. ∼H ⊃ ∼B
B
H
a. MT—valid.
b. Invalid.
c. MP—valid.
d. DS—valid.
e. DA—invalid.
31. ∼B ⊃ ∼J
∼J
∼B
a. DA—invalid.
b. AC—invalid.
c. MP—valid.
d. MT—valid.
e. DS—valid.
32. D ∨ M
(M ⊃ A) • (D ⊃ C)
A ∨ C
a. HS—valid.
b. Invalid.
c. DD—valid.
d. MP—valid.
e. CD—valid.
33. K ⊃ R
E ⊃ R
K ⊃ E
a. HS—valid.
b. CD—valid.
c. Invalid.
d. CD—invalid.
e. DA—invalid.
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34. F ⊃ ∼K
∼N ⊃ F
∼N ⊃ ∼K
a. MT—valid.
b. HS—valid.
c. Invalid.
d. DD—invalid.
e. CD—valid.
35. P ∨ G
(H ⊃ ∼P) • (C ⊃ ∼G)
∼H ∨ ∼C
a. CD—valid.
b. Invalid.
c. MT—valid.
d. DD—valid.
e. CD—invalid.
36. G ⊃ ∼R
G
∼R
a. DS—invalid.
b. MP—valid.
c. MT—valid.
d. DA—valid.
e. HS—valid.
37. ∼E ∨ ∼H
∼H
∼E
a. Invalid
b. CD—valid.
c. DD—valid.
d. CD—invalid.
e. MP—valid.
38. ∼Q ⊃ ∼R
Q
R
a. AC—invalid.
b. MP—valid.
c. HS—valid.
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d. MT—invalid.
e. DA—invalid.