Question

Show that every positive even integer is of the form 2q, and that every positive odd integer is of the form 2q+1, where q is some integer.

Answer 1

Let a be any positive integer and b=2. Then, by Euclid's division lemma there exist integers q and r such that

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

now, 0 = r <2

=> 0= r= 1

=> r=0 or, r=1 ( because r is an integer)

therefore a =2 q, then a is an even integer.

we know that an integer can either be even or odd. Therefore any odd integer is of the form 2q +1.

Answer 2

Hey sister !!!


here is your answer !!!

Let a be any positive integer and b =2

then by EDL ( eculid division leema )
there exist integers q and r



a = 2q + r. { where r is an integer }

now ,

0≤ r < 2

hence the number exist in form of

a = 2q

and a= 2q + 1

if a= 2q , where a is even integer

and a = 2q+1 , where a is odd integer .



=============


hope it helps you sister !!!


thanks