Question

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

Answer 1

To Show : The positive integers which are of the form 2q are even numbers and the positive integers which are of the form 2q+1 are odd numbers.

(Refer to the above attachment)

Answer 2

Euclid Division Algorithm :-

a = bq + r

Here a , b and q are integers.

★According to the situation of question we have to substitute 2 in the place of b and r = 0

So we have :-

a = 2q

★Here 2q is an even number.

Now :-

r = 1 and b = 2

a = bq + r

a = 2q + 1

★Here we get odd number.