Disjunction introduction

<h2 id="formal-notation">Formal notation</h2>
<p>The <i>disjunction introduction</i> rule may be written in <a href="/facts/Sequent/7YoB2hYb">sequent</a> notation:
</p>

P
        ⊢
        (
        P
        ∨
        Q
        )
      
    
    {\displaystyle P\vdash (P\lor Q)}

<p>where 
  
    
      
        ⊢
      
    
    {\displaystyle \vdash }
  
 is a <a href="/facts/Metalogic/zfooQjCo">metalogical</a> symbol meaning that 
  
    
      
        P
        ∨
        Q
      
    
    {\displaystyle P\lor Q}
  
 is a <a href="/facts/Logical_consequence/AyDXp4dn">syntactic consequence</a> of 
  
    
      
        P
      
    
    {\displaystyle P}
  
 in some <a href="/facts/Formal_system/KaeDAjK7">logical system</a>;
</p><p>and expressed as a truth-functional <a href="/facts/Tautology_(logic)/p82wWMaN">tautology</a> or <a href="/facts/Theorem/f2Pe1FMD">theorem</a> of propositional logic:
</p>

P
        →
        (
        P
        ∨
        Q
        )
      
    
    {\displaystyle P\to (P\lor Q)}

<p>where 
  
    
      
        P
      
    
    {\displaystyle P}
  
 and 
  
    
      
        Q
      
    
    {\displaystyle Q}
  
 are propositions expressed in some <a href="/facts/Formal_system/KaeDAjK7">formal system</a>.
</p>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>Hurley, Patrick J. (2014). A Concise Introduction to Logic (12th ed.). Cengage. pp. 401–402, 707. ISBN 978-1-285-19654-1. <a href="978-1-285-19654-1" target="_blank">978-1-285-19654-1</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>Moore, Brooke Noel; Parker, Richard (2015). "Deductive Arguments II Truth-Functional Logic". Critical Thinking (11th ed.). New York: McGraw Hill. p. 311. ISBN 978-0-07-811914-9. <a href="978-0-07-811914-9" target="_blank">978-0-07-811914-9</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>Copi, Irving M.; Cohen, Carl; McMahon, Kenneth (2014). Introduction to Logic (14th ed.). Pearson. pp. 370, 618. ISBN 978-1-292-02482-0. <a href="978-1-292-02482-0" target="_blank">978-1-292-02482-0</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
</ol>

Disjunction introduction open-in-new

Disjunction introduction