Final answer:
Awad's claim is false because when subtracting a negative integer (m) from a positive integer (n), the result can be positive if the magnitude of n is greater than the absolute value of m. A counterexample is n=3 and m=-2, which results in n-m = 5, a positive number.
Step-by-step explanation:
Awad's claim that when m is a negative integer and n is a positive integer, n-m is always negative is false. To understand why, consider that subtracting a negative number is the same as adding its positive counterpart. For instance, if we have n=3 (a positive integer) and m=-2 (a negative integer), then n-m would be 3 - (-2) = 3 + 2 = 5, which is a positive number. Thus, the sign of the result n-m will be determined by the magnitude of n relative to the absolute value of m. If n is greater than the absolute value of m, the result will be positive. This example serves as a counterexample to Awad's claim, demonstrating that n-m can be positive even when m is negative and n is positive.