CBSE Class 10 Answered
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