14. Another Demonstration



Answer:
Using the De Morgan Rule
    !(A && B) is equivalent to !A || !B
the original expression
    boolean reject = !(speed > 2000 && memory > 512)
is equivalent to


    boolean reject = !(speed > 2000) || !(memory > 512)
which is equivalent to
    boolean reject = (speed <= 2000) || (memory <= 512)


Another Demonstration











    





    
Here is the other De Morgan rule:





    

        
!(A || B) is equivalent to !A && !B

    





    
This truth table shows why this rule is true.

    
The fourth and the last column have the same truth values, which shows that the expressions at the top of those columns are equivalent.





    

        
            

                
                    
A

                		
                
                    
B

                		
                
                    
(A || B)

                		
                
                    
!(A || B)

                		
                
                    
!A

                		
                
                    
!B

                		
                
                    
!A && !B

                		
            

            

                
                    
F

                		
                
                    
F

                		
                
                    
F

                		
                
                    
T

                		
                
                    
T

                		
                
                    
T

                		
                
                    
T

                		
            

            

                
                    
F

                		
                
                    
T

                		
                
                    
T

                		
                
                    
F

                		
                
                    
T

                		
                
                    
F

                		
                
                    
F

                		
            

            

                
                    
T

                		
                
                    
F

                		
                
                    
T

                		
                
                    
F

                		
                
                    
F

                		
                
                    
T

                		
                
                    
F

                		
            

            

                
                    
T

                		
                
                    
T

                		
                
                    
T

                		
                
                    
F

                		
                
                    
F

                		
                
                    
F

                		
                
                    
F

                		
            

        
    






    





    
Question 14:
Rewrite the following fragment:
    while ( !(input.equals( "quit" ) || (count > limit)) ) 
{
   . . . 
}