Is the set of integers is close under subtraction?

Answer 1

Yes, because suppose that 'a' and 'b' are both arbitrary integers. Then (a-b) or (b-a) will then provide you with another integer. Suppose that the integer you are given from (a-b) is not unique. Then we have:

(a-b)=c

and

(a-b)=c'

Then, trivially, since (a-b)=(a-b), we have c=c'.

Thus it is closed under subtraction.

Answer 2

No.

To say a set is closed under subtraction means that if you subtract any 2 numbers in the set, the answer will always be a member of the set. If you subtract 3 from11, the answer is 8, which is not an odd number. Actually, when you subtract odd numbers, you always get an even number!