SOLUTION: Is this statement true or not? The set of even integers is closed under subtraction? Why or why not? Please help me im having hard time :(

Question 627835: Is this statement true or not?
The set of even integers is closed under subtraction? Why or why not?
Please help me im having hard time :(
Answer by reviewermath(1029) (Show Source): You can put this solution on YOUR website!
true:
Let the x and y be even integers, then
x = 2m for some integer m and
y = 2n for some integer n
Their difference is
x - y = 2m - 2n = 2(m - n)
Since x - y is a multiple of 2 then we can say that the set of even integers is closed under subtraction.

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