# Rutgers University Symbolic L

1. Use a truth tree or truth trees to determine whether it is possible for this sentence to be true. Explain your answer.

(B -> ~A) v A

2. Translate this prose sentence into formal notation and then use a truth tree or truth trees to determine whether it is possible for the sentence to be true. Explain your answer.

Either it is false that if I am a student then I love logic or both I am a student and if I am a student then I love logic.

3.Use a truth tree or truth trees to determine whether this sentence is a contingency, a contradiction, or a tautology. Explain your answer.

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

4. Translate this prose sentence into formal notation and then use a truth tree or truth trees to determine whether this sentence is a contingency, a contradiction, or a tautology. Explain your answer.

I am hungry, but I am tired; but if I am ornery, then I am both hungry and tired.

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

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

If and only if I am a student, then I love logic.

Both if I am a student, then I love logic, and if I love logic, then I am a student.

A -> B, ~B -> ~A

7. Use a truth tree or truth trees to determine whether this formal argument is valid or invalid. Explain your answer.

1. A v (B ^ C)

2. A

C. B -> ~C

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

If I will get a burrito for dinner, I will be happy tonight. If I am happy tonight, I will be productive tomorrow. I will be productive tomorrow. Therefore, I will get a burrito for dinner.

9.Translate this prose argument into formal notation and then use a truth tree or truth trees to determine whether the argument is valid or invalid and sound or unsound. Explain both of your answers. (“I” refers to you, the student.)

If I am a Rutgers–Camden student and I am taking logic, then I will study soundness. If I study soundness, then I study validity. I am a Rutgers–Camden student. I am taking logic. Therefore, I study validity.

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