1.

Show that every positive integer is either even or odd

Answer»

Step-by-step explanation:



let US assume that there exist a small positive integer that is neither odd or even, say n.



Since n is least positive integer which is neither even nor odd, n - 1 must be either or or even.



CASE 1 :



If n - 1 is even , then n - 1 = 2m for some integer m .



But , => n = 2m + 1 .



This implies n is odd .



CASE 2 :



If n - 1 is odd , then n - 1 = 2m + 1 for some integer m .



But, => n = 2m + 2 = 2( m + 1 ) .



This implies n is even .




In both cases , there is a CONTRADICTION .



THUS , every positive integer is either even or odd .




HENCE, it is solved




THANKS




#BeBrainly.


Discussion

No Comment Found

Related InterviewSolutions