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.