Second Translation Exercise

Answers

Translate the following English sentences into Propositional  Logic. Use ">" for the horseshoe and "iff" for the triplebar. 

1. He hated both man and beast.
   
   A: He hated man.
   B: He hated beast
   (A & B)
    
2. It is not true that he hated both man and beast.
   
   ~(A & B)
    
3. If it is false that he hated man, then he didn't hate beast
   
   (~A ⊃ ~B)
    
4. He hated neither man nor beast.
   
   (~A & ~B)
   
   alternatively:
   
   ~(A v B)
    
5. It is not the case that either he hated man or he hated beast.
   
   ~(A v B)
    
6. He didn't hate man or he didn't hate beast.
   
   (~A v ~B)
    
7. He hated man or beast, but not both.
   
   (A v B) & ~(A & B)
    
8. His hating man is a sufficient condition of his hating beast.
   
   (A ⊃ B)
    
9. He hated man only if he hated beast.
   
   (A ⊃ B)
    
10. He hated man if he hated beast.
    
    (B ⊃ A)
     
11. If Paul lodges a complaint, then Beth will investigate and Tom will be disqualified.
    
    P: Paul lodges a complaint
    B: Beth will investigate
    T: Tom will be disqualified
    
    P ⊃ (B & T)
     
12. If Paul lodges a complaint then Beth will investigate, and Tom will be disqualified.
    
    (P ⊃ B) & T
     
13. If Paul lodges a complaint then either Beth will investigate or Tom will be disqualified.
    
    (P ⊃ (B v T))
     
14. If Paul lodges a complaint and Beth investigates, then Tom will be disqualified.
    
    (P & B) ⊃ T
     
15. If either Paul lodges a complaint or Beth investigates, then Tom will be disqualified.
    
    (P v B) ⊃ T