Is the sum of two integers always greater than the difference between them? why or why not? give examples to support your answer.

Let x and y be the two integers. 

The sum of the integers is x+y while the difference is x-y assuming x is larger than y. 

If x+y > x-y, then 

x+y > x-y
x+y-x > x-y-x
y > -y
y+y > -y+y
2y > 0
2y/2 > 0/2
y > 0

So as long as y is positive, this makes the sum greater than the difference
For example, if x = 10 and y = 2, then
x+y = 10+2 = 12
x-y = 10-2 = 8
clearly 12 > 8 is true

If y is some negative number (say y = -4), then
x+y = 10+(-4) = 10-4 = 6
x-y = 10-(-4) = 10+4 = 16
and things flip around

Saying a blanket statement "the sum of two integers is always greater than their difference" is false overall. If you require y to be positive, then it works but as that last example shows, it doesn't always work. 

So to summarize things up, I'd say the answer is "no, the statement isn't true overall"

Ithink it's the first one ( let me know if it right)