real numbers

Asked by ashwinivg | 2nd Sep, 2009, 05:27: PM

Expert Answer:

Given: a and b are two odd numbers with a > b

\ a = 2k – 1 for some natural number k

and b = 2m – 1 for some natural number m

Now, 

Now k & m being natural numbers could have following 3 possibilities (i) both even (ii) both odd (iii) one even and one odd.

Case (i)      If both are even i.e., k, m are even

(A)     gives :( even number+ even number) – 1) = even number-1=odd number

(B)     gives: (even number – even number)= even number

Case (ii)     If k is even and m is odd or m is even and k is odd 

(A)     gives (even number +odd number) – 1 = odd number -1 = even number

(B)     gives even number – odd number = odd number

Case (iii)    If k and m are both odd

(A)     (odd number + odd number) – 1 = even number -1 = odd number

(B)     (odd number – odd number) = even number

 

 

 

 

 

 

Answered by  | 3rd Sep, 2009, 02:07: PM

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