Schoolcrop

(Q7).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.

Let a be any positive integer and b = 2.

Then, by division algorithm, a = 2q + r,

for some integer q > 0, and r = 0 or r = 1,

because 0 < r < 2. So, a = 2q or 2q + 1.

If a is of the form 2q, then a is an integer.

Also, a positive integer can be either even or .

it is in the form of 2q + 1, so it is called as positive integer.

Example => q = 1

= 2q + 1

= 2() + 1 =