Question

Show that every positive odd integer is of form 2q + 1

Answer 1

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Here, r can be equal or greater than zero but less than 2 at any cost. This possible values for r can be 0 or 1. Thus, a will be an even positive integer for 2q. Similarily, a will be an odd positive integer for 2q + 1.

Answer 2

(ii) Let 'a' be an odd positive integer. 

apply division algorithm with a and b, where b=2

a=(2×q)+r where 0≤r<2 

a=2q+r where r=0 or 1 

Here r=0 (∵a is not even) ⇒r=1

∴a=2q+1

Hence, a=2q+1 when 'a' is an odd positive integer.