Mathematical Logic


   
 
Summary
              -   A sentence is a statement if it is either true or false, but not both.
 
             -    The truth and falsity of a statement is its truth value.
 
            -   A truth table indicates the truth values of a number of statements and their compound statements in

                 a compact form.

 
           -    If there are n statements, then there are 2n rows in the truth table.
 
  •  
           -    The negation ~p of statement p is the denial of p.
 
           -    The conjunction 'p Ù q' of statements p and q is true only when p and q are both true.
 
           -    The disjunction 'p Ú q' of statements p and q is true if at least one of p and q is true.
 
           -   The conditional statement 'p ® q' of statements p and q (in this order) is true except when p is true and q is

                false.

           -   The biconditional statement 'p « q' of statements p and q is true only when p and q have same truth values.

 
  •  
      a) Idempotent laws
 
            -   p Ú p º p

            -   p Ù p º p

 
      b) Complement laws
 
         
 
       c) Identity laws
 
        
 
       d) Commutative laws
 
        
 
       e) De Morgan's laws
 
        
 
        f) Associative laws
 
        
 
        g) Distributive laws
 
        
 
  •  
         -    ~ (p Ù q) º ~ pÚ ~q

         -    ~ (p Ú q) º ~pÙ ~q

         -    ~ (p ® q) º pÙ ~q

         -    ~ (p « q) º (pÙ ~q) Ú (~p Ù q)

 
  •   Logical argument
         -    p1,p2, p3,... Q is valid if Q is true whenever p1, p2, p3,.... are all true, otherwise the argument is invalid.
 
  
     
   
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