For the product $mn$ to be even, at least one of the integers $m$ or $n$ must be even. This is because the product of two integers is even if at least one of them is even, while the product is odd only if both integers are odd.

Thus, the conditions for $mn$ to be even are:

• $m$ is even, or
• $n$ is even, or
• Both $m$ and $n$ are even.

Summary:

• $mn$ is even if either $m$ or $n$ is even.

Would you like further details or any examples? Here are some related questions to expand your understanding:

1. What are the properties of even and odd numbers when multiplied?
2. How do odd numbers behave when added or multiplied?
3. Can you provide examples of odd and even products?
4. What is the mathematical definition of even and odd numbers?
5. How does this condition change when working with real numbers instead of integers?

Tip: The product of two odd numbers is always odd.