Question

S. t. any even positive integer is in the form of 4q or 4q +2 where is a whole number

Answer 1

let 'a' be a even positive integer
by Euclid's lemma
a=bq+r b=4 r=0,1 ,2,3

if r=o
then a=4q+0
=4q (even)
if r =1
then a= 4q+1(odd)

if r=2
then a=4q+2(even)

if r=3
then a=4q+3(odd)
there fore any even positive integer is in the form of 4q,4q+2

Answer 2

Step-by-step explanation:

Let a be the positive integer.

And, b = 4 .

Then by Euclid's division lemma,

We can write a = 4q + r ,for some integer q and 0 ≤ r < 4 .

°•° Then, possible values of r is 0, 1, 2, 3 .

Taking r = 0 .

→ a = 4q .

Taking r = 1 .

→ a = 4q + 1 .

Taking r = 2

→ a = 4q + 2 .

Taking r = 3 .

→ a = 4q + 3 .

But a is an even positive integer, so a can't be 4q + 1 , or 4q + 3 [ As these are odd ] .

∴ a can be of the form 4q or 4q + 2 for some integer q .

Hence , it is solved