implication
noun
                                                                                                                            
                                                            im·pli·ca·tion
                    
                                                                                                              
                                                                                                                                  ˌim-plə-ˈkā-shən 
                                                      
                                                          
            1
                    
                  2
                    
        a
    
          
                                          
              
          
                                                      : close connection                                      
                
                                
            especially                
          
                                                      : an incriminating involvement                                      
            
            
        b
    
          
                                          
              
          
                                                      : the act of implicating : the state of being implicated                                      
                
                    
3
                    
        a
    
          
                                          
              
          
                                                      : the act of implying : the state of being implied                                      
                
                    
        b(1)
    
                
                                          
              
          
                                                      : a logical relation between two propositions that fails to hold only if the first is true and the second is false   see Truth Table                                      
                
                    
        (2)
    
                
                                          
              
          
                                                      : a logical relationship between two propositions in which if the first is true the second is true                                      
                
                    
        (3)
    
          
                                          
              
          
                                                      : a statement exhibiting a relation of implication                                      
                
                    
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  Merriam-Webster unabridged




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