Mathematical Induction


   
 
Statement
A sentence which is either true or false is called a statement.
 
Examples:
 
(1) " January has 31 days” is a statement.
 
(2) "Null set is a subset of every set” is a statement.
 
(3) "All girls are studious” is not a statement.
 
(4) "Apoorva is honest” is not a statement.
 
Some sentences depend on a variable for its truth value (i.e., true or false).
 
e.g., “2+4+6+…2n=2n” is true for n=1 but false for n=2, n=3 etc.
 
As the above sentence is definitely true or definitely false for a particular positive integral value of n, the sentence is a statement and it depends on for its truth-value. Such statements are called predicates and are symbolised as P(n).
 
 
     
   
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