Symbolic Logic/ Philosophy questions: contingency, a contradiction, a tautology
- 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)
- 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)
- 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.
- 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
- 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
- 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.
- Use a truth table to determine whether this formal argument is valid or invalid. Explain your answer.
- (A ^ B) -> C
- A -> B
- A
C. C
- 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.
- 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.