Mathematical Logic Summary


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-   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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