Propositional Logic Functions

Answers

1. 
   
   • a. P = Coral is a plant; A = Coral is an animal
   • b. ~(P ⋅ A)
   • c. Main operator is the negation
2. 
   
   • a. A = Protozoa are eukaryotes; B = Chimpanzees are eukaryotes; C
   • = Protozoa are animals; D = Chimpanzees are animals
   • b. (A ⋅ B) ⋅ ~(C ⋅ D)
   • c. Main operator is the second dot
3. 
   
   • a. C = Chimpanzees are prokaryotes; P = Protozoa are prokaryotes
   • b. ~(C v P)
   • c. Main operator is the negation
4. 
   
   • a. C = China has not signed the Kyoto Protocol; U = The United States has not signed the Kyoto Protocol
   • b. ~(C v U)
   • c. Main operator is the negation
5. 
   
   • a. C = Chevrolet will support the Olympic team; M = McDonald’s will support the Olympic team
   • b. (C v M) ⋅ ~(C ⋅ M)
   • c. Main operator is the first dot
6. 
   
   • a. L = Peter Jennings is a liar; M = Peter Jennings has a really bad memory
   • b. L v M
   • c. Main (and only) operator is the wedge
7. 
   
   • a. L = Peter Jennings is a liar; M = Peter Jennings has a really bad memory
   • b. ~(L v M)
   • c. Main operator is the negation
8. 
   
   • a. L = Peter Jennings is a liar; M = Peter Jennings has a really bad memory
   • b. L ⋅ M
   • c. Main (and only) operator is the dot
9. 
   
   • a. L = Peter Jennings is a liar; M = Peter Jennings has a really bad memory
   • b. ~(L ⋅ M)
   • c. Main operator is the negation
10. 
    
    • a. C = Chevrolet will support the Olympic team this year; M = McDonald’s will support the Olympic team this year
    • b. ~(C v M)
    • c. Main operator is the negation
11. 
    
    • a. S = Mother Theresa is a saint; C = Mother Theresa has been canonized by the Catholic Church
    • b. S ⋅ ~C
    • c. Main operator is the dot
12. 
    
    • a. T = Paul Tergat was the best distance runner of the last two decades; G = Haile Gebrselassie was the best distance runner of the last two decades; R = Jim Ryun was the best distance runner of the last two decades
    • b. (T v G) ⋅ ~R
    • c. Main operator is the dot
13. 
    
    • a. R = Jim Ryun was the best high school miler of all time; W = Jim Ryun ran a slower time than Alan Webb
    • b. R ⋅ W
    • c. Main (and only) operator is the dot
14. 
    
    • a. A = Paul Tergat knows how to play hockey; B = Haile Gebrselassie knows how to play hockey; C = Paul Tergat knows how to play soccer; D = Haile Gebrselassie knows how to play soccer
    • b. ~(A v B) ⋅ (C ⋅ D)
    • c. Main operator is the first dot
15. 
    
    • a. B = Ethiopians are good bobsledders; T = Ethiopians are good tennis players; D = Ethiopians are good distance runners
    • b. ~(B v T) ⋅ D
    • c. Main operator is the dot
16. 
    
    • a. S = Before Helen Keller met Annie Sullivan she could speak; R = Before Helen Keller met Annie Sullivan she could read; C = Before Helen Keller met Annie Sullivan she could communicate
    • b. (~S ⋅ ~R) ⋅ ~C
    • c. Main operator is the second dot
17. 
    
    • a. C = Helen Keller learned to communicate; S = Helen Keller learned to play soccer; B = Helen Keller learned to play baseball
    • b. C ⋅ (~S ⋅ ~B)
    • c. Main operator is the first dot
18. 
    
    • a. F = Tom is allowed to play football; S = Tom is allowed to play soccer
    • b. (F v S) ⋅ ~(F ⋅ S)
    • c. Main operator is the first dot
19. 
    
    • a. E = Tom will major in engineering; P = Tom will major in physics; B = Tom will major in business; S = Tom will major in sociology
    • b. (E ⋅ P) v (B ⋅ S)
    • c. Main operator is the wedge
20. 
    
    • a. X = Cartman is xenophobic; R = Cartman is a racist; M = Cartman is a murderer; T = Cartman is the thief
    • b. (X ⋅ R) ⋅ (~M ⋅ ~T)
    • c. Main operator is the second dot