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  M5.A1 Truth Table Exercises          Back-Up QUESTION SET                                                 1Premise:P †’ Q           Conclusion:~P †’ ~Q                        Answer:                                      PQ                             

  M5.A1 Truth Table Exercises          Back-Up QUESTION SET                                                 1Premise:P †’ Q           Conclusion:~P †’ ~Q                        Answer:                                      PQ                             

 

M5.A1 Truth Table Exercises                    
Back-up QUESTION SET                    
                         
                         
                         
1 Premise: P → Q                    
  Conclusion: ~P → ~Q                    
                         
  Answer:                      
                         
                         
  P Q                    
                         
                         
                         
                         
                         
                         
                         
2 Premise: P → Q                    
  Conclusion: ~Q → ~P                    
                         
  Answer:                      
                         
                         
  P Q                    
                         
                         
                         
                         
                         
                         
3 Premise: (P & Q) → R                    
    Q   R                    
  Conclusion: P   R                    
                         
P Q R                    
                         
                         
                         
                         
                         
                         
                         
                         
                         
                         
4 Translate the following argument and use truth tables to test for validity.            
             
                         
  “If 9 is less than 10 and every odd number less than 10 is divisible by 3, then 9 is divisible by 3. THEREFORE If 9 is less than 10 it is less than 10 it is divisible by 3.”
 
 
                         
  N = “9 is less than 10”                    
  O = “Every odd number less than 10 is divisible by 3.”            
  D =  “9 is divisible by 3.”                    
                         
  Premise:                      
  Conclusion:                      
                         
N O D                    
                         
                         
                         
                         
                         
                         
                         
                         
                         
5. Translate the following argument and use truth tables to test for validity.        
       
       
  “If it rains tomorrow, I will have a tough commute. If it snows tomorrow, I will have a tough commute. It will either rain or snow tomorrow. THEREFORE I will have a tough commute.”
 
 
                         
  R = “It rains tomorrow.”                
  S = “It snows tomorrow.”                
  T = “I will have a tough commute.”              
                         
  Premise:                       
                         
                         
  Conclusion     ANSWER:             
                         
R S T                    
                         
                         
                         
                         
                         
                         
                         
                         
                         
                         
                         
                         
                         
                         
                         
                         
                         
                         
                         
                         
                         
                         
                         
                         
                         
                         
                         
                         
                         
                         
                         
                         
                         
                         
                         
                         
                         
                         
                         
                         
                         

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