Directions: Translate each sentence into propositional logic using the propositional variables given after the sentence. 1. The restaurant served chicken, and either peas or carrots. (C, P,T) 2. Making butter is a necessary condition for the farmer to go to the market and make a profit. (B, M,P) 3. Patrons may have corn and potatoes if, and only if, they do not order carrots, (C, P, T) 4. If the restaurant runs out of cheesecake, then you can have a meal of chicken and pie and ice cream. (G, S, D, C) 5. A farmer keeps goats in a pen and sheep in a pen only if the dogs and cat are kept inside. (G. S, D, C) 6. Either the farmer shears the sheep and milks the cows, or he slops the pigs and walks the dog. (S, C, P, D) 7. If the farmer shears the sheep, then he makes the wool, and if he milks the cows, then he makes the butter. (S, W, C, B) 8. If the farmer goes to the marker, then she makes a profit. and her wife is happy. (M. P. W) 9. Plato believed in the theory of forms, and Aristotle held that there are four kinds of causes. but Parmenides thought that only the one exists. (P, A, R) 0. If Thales reduced everything to water, then Democritus was an atomist if and only if Heraclitus claimed that the world is constantly in flux. (T, D, H) 1. If Piato believed in the theory of forms or Democritus was an atomist, then Aristotle help that there are four kinds of causes or Parmenides thought that oniy the one exists. (P,D,A,R)