I. Translate the following statements into symbolic form using uppercase letters to represent affirmative English statements.
Example: Suppose you are given the statement “If Facebook makes us narcissistic, then either Twitter or LinkedIn relieves our loneliness.” This would be translated F ⊃ (T ¡ L).
11. Bill Gates does not support malaria research unless Warren Buffet does.
12. Mercedes will introduce a hybrid model only if Lexus and BMW do.
13. Mariah Carey sings pop and either Elton John sings rock or Diana Krallsings jazz.
14. Either Mariah Carey sings pop and Elton John sings rock or Diana Krall sings jazz.
15. Not both Jaguar and Porsche make motorcycles.
16. Both Jaguar and Porsche do not make motorcycles.
17. Either Apple or Samsung makes smartphones.
18. Not either Ferrari or Maserati makes economy cars.
19. Neither Ferrari nor Maserati makes economy cars.
20. Either Ferrari or Maserati does not cars
Determine which of the following are not well-formed formulas.
1. (S ∼T)¡(∼U W) ●
2.∼(K¡L) (⊃G¡H)
3. (E∼F)¡(WKX)
4. (B⊃∼T)K∼(∼C⊃U)
5. (FK∼Q) (A⊃E¡T)
7. [(D ¡ Q)⊃(P¡ E)]¡ [A⊃( H)] ●●
8. M(N⊃Q)¡(∼C D)●●
9. ∼(F¡∼G)⊃[(AKE) ∼H]
10. (RKS● T)⊃∼(∼W● ∼X)IV.
Construct compound propositions involving at least three simple propositions about the following topics. Then, symbolize your propositions as per Parts I and II of this exercise.
1. Political figures
2. NFL teams
3. Corporations
4. Brands of automobiles
5. Music or film celebrities
Write the following compound statements in symbolic form, then use your knowl- edge of the historical events referred to by the simple statements to determine the truth value of the compound statements.
1. It is not the case that Hitler ran the Third Reich.
2. Nixon resigned the presidency and Lincoln wrote the Gettysburg Address.
3. France bombed Pearl Harbor, or Lindbergh crossed the Atlantic.
4. Hitler ran the Third Reich and Nixon did not resign the presidency.
5. Edison invented the telephone, or Custer was killed by the Indians.
6. Julius Caesar conquered America if Napoleon ruled France.
7. Washington was assassinated only if Edison invented the telephone.
8. Lincoln wrote the Gettysburg Address if and only if France bombed Pearl
Harbor.
9. It is not the case that either Julius Caesar conquered America or Washington was assassinated.
10. If Hitler ran the Third Reich, then either Custer was killed by the Indians or Einstein discovered aspirin.
11. Either Lindbergh crossed the Atlantic and Edison invented the telephone or both Nixon resigned the presidency and it is false that Edison invented the telephone.
12. Lincoln’s having written the Gettysburg Address is a sufficient condition for Julius Caesar’s having conquered America if and only if Washington’s being assassinated is a necessary condition for Custer’s having been killed by the Indians.
13. Both Hitler ran the Third Reich and Lindbergh crossed the Atlantic if neither Einstein discovered aspirin nor France bombed Pearl Harbor.
14. It is not the case that Custer was killed by the Indians unless both Nixon resigned the presidency and Edison invented the telephone.
15. Custer was killed by the Indians, and Lincoln wrote the Gettysburg Address only if either Washington was assassinated or Julius Caesar conquered America
Translate each sentence into propositional logic using the propositional variables given after the sentence.
The restaurant served chicken, and either peas or carrots. (C, P, T)
Making butter is a necessary condition for the farmer to go to the market and make a profit. (B, M, P)
Patrons may have corn and potatoes if, and only if,farmer to go to the market and make a profit. (B, M, P)
Patrons may have corn and potatoes if, and only if, they do not order carrots. (C, P, T)
If the restaurant runs out of cheesecake, then you can have a mea n of chicken and pie and ice cream. (G, S, D, C)
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)
Either the farmer shears the sheep and milks the cows, or he slops the pigs and walks the dog. (S, C, P, D)
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)
If the farmer goes to the marker, then she makes a profit, and her wife is happy. (M, P, W)
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)
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)
If Plato 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 only the one exists. (P, D, A, R)
