Step-by-step:
- Take two positive integers. Call them (a) and (b).
- Because they are positive: (a \ge 1\).
- Also: (b \ge 1\).
- Add them: (a + b\).
- Since (b \ge 1\), we get (a + b \ge a + 1\).
- And (a + 1 > a\). So (a + b > a\).
- Similarly, since (a \ge 1\), we get (a + b \ge b + 1\).
- And (b + 1 > b\). So (a + b > b\).
- Example: (3 + 5 = 8\); here (8 > 3\) and (8 > 5\).
Conclusion: The sum of two positive integers is greater than each of them. So the statement is true.