I’m working on a philosophy multi-part question and need an explanation to help me study.

2. Use a truth table to determine whether this formal sentence is a contingency, a contradiction, or a tautology (remember, ‘or’ is inclusive). Explain your answer.

(A -> B) -> (B -> A)

3. Use a truth table to determine whether this formal sentence is a contingency, a contradiction, or a tautology (remember, ‘or’ is inclusive). Explain your answer.

~(A ^ B) <-> (~A v ~B)

4. Translate this prose sentence into formal notation and then use a truth table to determine whether the formal sentence is a contingency, a contradiction, or a tautology (remember, ‘or’ is inclusive). Explain your answer.

If both I am tired and I am hungry, then I am annoyed; but if I am tired and I am not hungry, I am not annoyed.

5. Use a truth table to determine whether this set of formal sentences is consistent, contradictory, or equivalent (remember, ‘or’ is inclusive). Explain your answer.

A -> (B v C), ~(B v C) ^ A

6. Use a truth table to determine whether this set of formal sentences is consistent, contradictory, or equivalent (remember, ‘or’ is inclusive). Explain your answer.

A -> B, ~A v B, ~B -> ~A

7. Translate these prose sentences into formal notation and then use a truth table to determine whether the set of formal sentences is consistent, contradictory, or equivalent (remember, ‘or’ is inclusive). Explain your answer.

If I am a student, then I am not a professor.

Either I am a student or I am a professor.

I am neither a student nor a professor.

8. Use a truth table to determine whether this formal argument is valid or invalid. Explain your answer.

1. (A ^ B) -> C

2. A -> B

3. A

C. C

9. Translate this prose argument into formal notation and then use a truth table to determine whether the formal argument is valid or invalid. Explain your answer.

I am a student if and only if I am learning. I am learning only if my knowledge is expanding. Therefore, if my knowledge is expanding, I am a student.

10. Determine whether this argument is valid or invalid and sound or unsound. Explain both of your answers.

Both if this is a philosophy class then we study argument and if this is a logic class then we study arguments. We study arguments. Therefore, this is a philosophy class and this is a logic class.