Logical equivalence

<p>In <a href="/facts/Logic/8JnpJLtt">logic</a> and <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, statements 
  
    
      
        p
      
    
    {\displaystyle p}
  
 and 
  
    
      
        q
      
    
    {\displaystyle q}
  
 are said to be logically equivalent if they have the same <a href="/facts/Truth_value/SY4e2w8l">truth value</a> in every <a href="/facts/Model_(logic)/GsMx1fEb">model</a>. The logical equivalence of 
  
    
      
        p
      
    
    {\displaystyle p}
  
 and 
  
    
      
        q
      
    
    {\displaystyle q}
  
 is sometimes expressed as 
  
    
      
        p
        ≡
        q
      
    
    {\displaystyle p\equiv q}
  
, 
  
    
      
        p
        ::
        q
      
    
    {\displaystyle p::q}
  
, 
  
    
      
        
          
            E
          
        
        p
        q
      
    
    {\displaystyle {\textsf {E}}pq}
  
, or 
  
    
      
        p
        
        ⟺
        
        q
      
    
    {\displaystyle p\iff q}
  
, depending on the notation being used.
However, these symbols are also used for <a href="/facts/Material_equivalence/bYSxGJ66">material equivalence</a>, so proper interpretation would depend on the context. Logical equivalence is different from material equivalence, although the two concepts are intrinsically related.
</p>

Logical equivalence open-in-new

Logical equivalence