Question

show that any positive even integer can be written in the form 6Q, 6 Q + 2 or 6 Q + 4 where Q is an integer​

Answer 1

Answer:

a=bq+r

6q-even

6q+1-odd

6q+2-even

6q+3-odd

6q+4-even

From the above statement we know that 6q, 6q+2,6q+4 is a positive even integer where q is some integer

Answer 2

your solution is below :

Let ‘a’ be any positive even integer and ‘b = 6’.

Therefore, a = 6q +r, where 0 ≤ r < 6.

Now, by placing r = 0, we get, a = 6q + 0 = 6q

By placing r = 1, we get, a = 6q +1

By placing, r = 2, we get, a = 6q + 2

By placing, r = 3, we get, a = 6q + 3

By placing, r = 4, we get, a = 6q + 4

By placing, r = 5, we get, a = 6q +5

Thus, a = 6q or, 6q +1 or, 6q + 2 or, 6q + 3 or, 6q + 4 or, 6q +5.

But here, 6q +1, 6q + 3, 6q +5 are the odd integers.

Therefore, 6q or, 6q + 2 or, 6q + 4 are the forms of any positive even integers.

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