Translate the following English sentences into symbolic logic sentences using the constants indicated. Make sure you write out what the atomic propositions are. In some cases this will be straightforward, but not in every case. Remember: atomic propositions never contain any truth functional connectives—and that includes negation! Note: although many of these sentences can be translated using only the horseshoe, others require truth functional connectives other than the horseshoe
1. The Tigers will win only if the Indians lose their star pitcher. (T, I)
2. Tom will pass the class provided that he does all the homework. (P, H)
3. The car will run only if it has gas. (R, G)
4. The fact that you are asking me about your grade implies that you care about your grade. (A, C)
5. Although Frog will swim without a bathing suit, Toad will swim only if he is wearing a bathing suit. (F, T, B)
6. If Obama isn’t a U.S. citizen, then I’m a monkey’s uncle. (O, M)
7. If Toad wears his bathing suit, he doesn’t want Frog to see him in it. (T, F)
8. If Tom doesn’t pass the exam, then he is either stupid or lazy. (P, S, L)
9. Bekele will win the race as long as he stays healthy. (W, H)
10.If Bekele is either sick or injured, he will not win the race. (S, I, W)
11.Bob will become president only if he runs a good campaign and doesn’t say anything stupid. (P, C, S)
12.If that plant has three leaves then it is poisonous. (T, P)
13.The fact that the plant is poisonous implies that it has three leaves. (T, P)
14.The plant is poisonous only if it has three leaves. (T, P)
15.The plant has three leaves if it is poisonous. (T, P)
16.Olga will swim in the open water as long as there is a shark net present. (O, N)
17.Olga will swim in the open water only if there is shark net. (O, N)
18.The fact that Olga is swimming implies that she is wearing a bathing suit. (O, B)
19.If Olga is in Nice, she does not wear a bathing suit. (N, B)
20.If Terrence pulls Philip’s finger, something bad will happen. (T, B)
1. T ? I (T = The Tigers will win; I = The Indians will lose their star pitcher)
2. H ? P (P = Tom will pass the class; H = Tom does all of his homework)
3. R ? G (R = The car will run; G = The car has gas)
4. A ? C (A = You are asking me about your grade; C = You care about your grade)
5. F ? (T ? B) (F = Frog will swim without his bathing suit; T = Toad will swim; B = Toad is wearing a bathing suit)
6. ~O ? M (O = Obama is not a U.S. citizen; M = I am a monkey’s uncle)
7. T ? ~F (T = Toad wears his bathing suit; F = Toad wants Frog to see him in his bathing suit)
8. ~P ? (S v L) (P = Tom passes his exam; S = Tom is stupid; L = Tom is lazy)
9. H ? W (W = Bekele will win the race; H = Bekele stays healthy)
10. (S v I) ? ~W (S = Bekele is sick; I = Bekele is injured; W = Bekele will win the race)
11. P ? (C ? ~S) (P = Bob will become president; C = Bob runs a good campaign; S = Bob says something stupid)
12. T ? P (T = That plant has three leaves; P = That plant is poisonous)
13. P ? T (T = That plant has three leaves; P = That plant is poisonous)
14. P ? T (T = That plant has three leaves; P = That plant is poisonous)
15. P ? T (T = That plant has three leaves; P = That plant is poisonous)
16. N ? O (O = Olga will swim in the open water; N = There is a shark net present)
17. O ? N (O = Olga will swim in the open water; N = There is a shark net present)
18. O ? B (O = Olga is swimming; B = Olga is wearing a bathing suit)
19. N ? ~B (N = Olga is in Nice; B = Olga wears a bathing suit)
20. T ? B (T = Terrence pulls Philip’s finger; B = Something bad will happen)
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