1. If an argument is valid but not sound, which one of the following is not possible?

a. All the premises of the argument are true.

b. The conclusion of the argument is true.

c. The conclusion of the argument is false.

d. All the premises of the argument are false.

2. Using the truth table method, determine whether the following argument is valid or invalid.

¬P  ¬Q, ¬R → Q ：¬(¬R  ¬¬P)

a. Valid

b. Invalid

3. Suppose ¬A  (¬B  ¬C) is true and A and B are true. What can we know about C? (A, B, C are not metavariables)

a.it is false

b.it is a contradiction

c.it is true

d.it is a tautology

4. Suppose ((A 个 B) ⟷ ¬A) is false, and A is true. What can we know about B? (A, B are not metavariables)

a.It is true

b. It is false

c. It is a tautology

d. It cannot be determined

5. Suppose that B is a tautology. What can you say about whether A, B ╞ C? (Note that A, B, and C

are metavariables.)

a. The entailment holds.

b. The entailment holds only if C is not contingent.

c. The entailment holds only ifA is contingent.

d. The entailment holds ifA is a contradiction.

6.   Suppose that A and B areequivalent. What can you say about (A  ¬B) → ¬(A ⟷ B)? (Note thatA and B are metavariables.)

a. It is a tautology.

b. It is a contradiction.

c. It is a contingent sentence.

7. Suppose that A, B, and C arejointly satisfiable. What can you say about (A  (B  C))? (Note that A, B, and C are metavariables.)

a. It is not a contradiction.

b. It is a tautology.

c. It is not a tautology.

d. It is a contingent sentence.

Using the following translation key, choose the correct translation into TFL.

A: Ann is a student.

B: Ben is a student.

C: Cindy is a student.

8. “The necessary condition for both Ben and Cindy to be students is that Ann is a student” .

a.  A ↔ (B  C)

b.  A → (B  C)

c.   (B  C) V A

d.  (B  C) → A

9. “For Cindy to be a student, it is sufficient that neither Ann nor Ben are students” .

a. (¬A  ¬B) → C

b. C →  (¬A  ¬B)

c. ¬(A  B) → C

d. (¬A  ¬B)  C

10.       “At most one, between Cindy and Ben, is a student; however, Ann is not a student” .

a. (¬B ∧ ¬C) ∧ ¬A

b. A → ¬(B ∧ C)

c. ¬(B ∧ C) ∧ ¬A

d. ¬((B ∧ C) ∧ ¬A)

11.     “At least two between Ann, Ben and Cindyare students”.

a. ¬(A ∧ (B V C))

b. A ∨ (B ∨ C)

c. (A ∧ B) ∨ ((B ∧ C) ∨ (A ∧ C))

d. ¬(A ∧ (B ∧ C))

12. Cindy is a student, provided Ann is not a student.

a. A → ¬ C

b. ¬A ⟷ C

c. C  ¬A

d. ¬A → C

13.    Is the following expression a correct TFL-sentence?

A ↔ ((B  ¬¬C) ↔ D)

Yes

No

14.    Which one of the following expressionsis a correct TFL-sentence?

a. (S ↔ (Q ∨ ¬(P → ¬R))) ∧ L

15.    Find the main connective in the following TFL-sentence.

(A → (A ∨ (B ∧ (C ↔ D))))

16.    Find the main connective in the following TFL-sentence.

¬(A  (B → C))  (C ↔  D)