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.

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.

anonymous · Answer

hint  : 6k0−6k1=6(k0−k1) where k1,k0 are integers.

anonymous · Answer

@Le_Asien

anonymous · Answer

so d i;m thinking

anonymous · Answer

I think you're right.

anonymous · Answer

I would listen to her, I dont know this at all, I have never seen this

geerky42 · Answer

So -12 is not multiple of 6?

Weird... because $-12 = -2\cdot6$