Question

Is the set of numbers that can be written as the product of 6 and an integer closed under subtraction?

A.
Yes, because the difference of any two multiples of 6 is equal to 6.

B.
Yes, because the difference of any two multiples of 6 is also a multiple of 6.

C.
No, and a counterexample is 6 – 6 = 0.

D.
No, and a counterexample is 6 – 18 = –12.

Answer 1

what does closed mean?

Answer 2

we are not going to just give answers, so you need to understand it, or at least try....

Answer 3

ok I understand

Answer 4

if you take any multiply of 6 and subtract a multiple of 6, do you have a multiple of 6?

Answer 5

hint : \(6k_0-6k_1=6(k_0-k_1)\) where \(k_1,k_0\) are integers.

so the question becomes, are the integers closed with respect to subtraction

Answer 6

umm......yes

Answer 7

why?