Question

Show that any positive
integer is of the form
3 q, 3q+1 or 3 q + 2 for
some integer q.​

Answer 1

Answer:

Let A be any positive integer,

now, by Euclids Division Lemma,

"a=bq+r"

now, b=3

therefore, 'r' should be 0, 1 or 2 {B'coz 0<r}

now, when r = 0

then,

a=3q+r

a=3q+0

a=3q

========

when r = 1

a=3q+r

a=3q+1

========

when r = 2

a=3q+r

a=3q+2

HENCE PROVED

Answer 2

Fallow Lands other than Current Fallows : This includes all land which was taken up for cultivation but is temporarily out of cultivation for a period of not less than one year and not more than five years. Current Fallows: This represents cropped area which is kept fallow during the current year.