Let's analyze the statements regarding subtraction of integers:
-
A positive integer minus a positive integer will always have a positive solution.
- This is false. For example, \(5 - 3 = 2\) (positive), but \(3 - 5 = -2\) (negative).
-
A negative integer minus a positive integer will always have a positive solution.
- This is false. For example, \(-2 - 3 = -5\) (negative).
-
A negative integer minus a negative integer will always have a negative solution.
- This is false. For example, \(-3 - (-5) = -3 + 5 = 2\) (positive).
-
A positive integer minus a negative integer will always have a positive solution.
- This is true. For example, \(5 - (-3) = 5 + 3 = 8\) (positive).
Based on the analysis, the only true statement is:
A positive integer minus a negative integer will always have a positive solution.