Question

show that every positive even integer is of the form 2q , and that every positive odd integer is of form 2q +1. by q is some integer​

Answer 1

Answer:

hey there !

have a look at your answer......

let 'a' be any positive integer and b=2

By euclid's division algorithm

a=bq+r       0≤r<b

a=2q+r       0≤r<2

(i.e) r =0,1

r=0 , a=2q+0=> a=2q

r=1, a=2q+1

if a is the form of 2m then 'a' is an even integer and positive odd integer is of the form 2m+1

hope it helps you deaR !

✌✌

plz like and mark brainliest !!!

Answer 2

Answer:

Let a be any given positive integer.

On dividing a by 2, let q be the quotient and r be the remainder.

By Euclid's Division Lemma, we have

             a = 2q + r, where 0 ≤ r < 2

             a = 2q + r,  r = 0, 1

(i) r = 0

⇒ a = 2q + 0

⇒ a = 2q - Even number

(ii) r = 1

⇒ a = 2q + 1  - Odd number

_______________________

Hope it helps you!!

:)