1. Use a truth tree or truth trees to determine whether it is possible for this sentence to be true. Explain your answer.
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A -> ~(B -> C)
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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.
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It is false that either if I am a student then I love logic or if I am a student then I do not love logic.
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3. Use a truth tree or truth trees to determine whether this sentence is a contingency, a contradiction, or a tautology. Explain your answer.
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(A -> B) ^ (~A v ~B)
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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.
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If I’m tired then I’ll take a nap, but if I’m not tired then I won’t take a nap.
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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.
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A ^ B, ~(~A ^ ~B)
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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.
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Unless I cook dinner, I have to order delivery.
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If I have to order delivery, then I do not cook dinner.
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7. Use a truth tree or truth trees to determine whether this formal argument is valid or invalid. Explain your answer.
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1. A v (B v C)
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2. ~(~A v ~B)
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C. C
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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.
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If I study hard, then I will get a good grade. I will get a good grade. Therefore, I study hard.
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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.)
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I love burrata if and only if I have decent taste. I have decent taste. Therefore, either I love burrata or I really love burrata.
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