#### If a and b are positive integers, then a + b is also a positive integer.

This theorem states that if a and b are positive integers, then their sum a + b is also a positive integer. This is true because both a and b are positive, so their sum must be positive as well.

#### Problem

`Prove that if a and b are positive integers, then a + b is also a positive integer.`

#### Solution

`This is a direct result of the definition of addition for integers. For two integers a and b, a + b is defined as the sum of a and b. This sum will always be an integer, as it is the result of adding two integers. Therefore, a + b will always be a positive integer.`

A.I. Evaluation of the Solution

The candidate's solution is correct and demonstrates a level of completeness. The candidate has correctly identified that this is a direct result of the definition of addition for integers. The candidate has also correctly identified that the sum of two integers will always be an integer. Therefore, the candidate's solution solves the problem and is a correct approach.

Evaluated at: 2022-11-11 17:18:36