Mathematical Logic


   
 
Application of Logic in solving simple problems
Argument
 
An argument is a statement which assets that a given set of n compound statements p1,p2,..........pn yield another compound statement Q.
 
This is denoted by
 
 
where p1,p2,..........pn are called hypotheses or premises or assumptions.
 
The compound statement Q is called the conclusion.
 
 

The argument p1, p2,...., pn Q is defined to be true if Q is true whenever p1,p2,..........pn are all true.

 
Otherwise, the argument is defined to be false.
 
A true argument is also called a valid argument.
 
Useful steps for solving problems:
 
Step i: Identify the component statements in the given argument and denote these as p, q, r,……
 
Step ii: Identify the assumptions and denote these as p1,p2,p3....
 
Step iii: Identify the conclusion as Q.
 
Step iv: Express p1,p2,p3...., Q in terms of p, q, r,……
 
Step v: Find the truth values of p1,p2,p3...., Q
 
Step vi: If Q is true whenever p1,p2,p3.... are all true, then the argument p1, p2,... Q is valid, otherwise it is invalid.
 
 
     
   
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