Sheffer stroke

<p>In <a href="/facts/Boolean_function/uT7E8pqC">Boolean functions</a> and <a href="/facts/Propositional_calculus/MNt5v31V">propositional calculus</a>, the Sheffer stroke denotes a <a href="/facts/Logical_operation/VkPhUs6M">logical operation</a> that is equivalent to the <a href="/facts/Logical_negation/q5AQBvBj">negation</a> of the <a href="/facts/Logical_conjunction/62uyyn1d">conjunction</a> operation, expressed in ordinary language as "not both". It is also called non-conjunction, or alternative denial (since it says in effect that at least one of its operands is false), or NAND ("not and"). In <a href="/facts/Digital_electronics/3kJcKbkw">digital electronics</a>, it corresponds to the <a href="/facts/NAND_gate/g6FUuhJT">NAND gate</a>. It is named after <a href="/facts/Henry_Maurice_Sheffer/YF8RpQKG">Henry Maurice Sheffer</a> and written as 
  
    
      
        ∣
      
    
    {\displaystyle \mid }
  
 or as 
  
    
      
        ↑
      
    
    {\displaystyle \uparrow }
  
 or as 
  
    
      
        
          
            ∧
            ¯
          
        
      
    
    {\displaystyle {\overline {\wedge }}}
  
 or as 
  
    
      
        D
        p
        q
      
    
    {\displaystyle Dpq}
  
 in <a href="/facts/Polish_notation/dUzpf2Ys">Polish notation</a> by <a href="/facts/Jan_%25C5%2581ukasiewicz/1rlu9ej8">Łukasiewicz</a> (but not as ||, often used to represent <a href="/facts/Logical_disjunction/jbI2EGlM">disjunction</a>).
</p><p>Its <a href="/facts/Duality_(mathematics)/8jGuyQIU">dual</a> is the <a href="/facts/Logical_NOR/HKhNW8Qc">NOR operator</a> (also known as the <a href="/facts/Peirce_arrow/HKhNW8Qc">Peirce arrow</a>, <a href="/facts/Quine_dagger/HKhNW8Qc">Quine dagger</a> or <a href="/facts/Webb_operator/HKhNW8Qc">Webb operator</a>). Like its dual, NAND can be used by itself, without any other logical operator, to constitute a logical <a href="/facts/Formal_system/KaeDAjK7">formal system</a> (making NAND <a href="/facts/Functionally_complete/ncyHAsHH">functionally complete</a>). This property makes the <a href="/facts/NAND_gate/g6FUuhJT">NAND gate</a> crucial to modern <a href="/facts/Digital_electronics/3kJcKbkw">digital electronics</a>, including its use in <a href="/facts/Computer_processor/Jxp1bqMV">computer processor</a> design.
</p>

Sheffer stroke open-in-new

Sheffer stroke