Answer:
See below (I hope this helps!)
Step-by-step explanation:
Because odd numbers are always 1 greater than even numbers, we can call the two odd numbers x + 1 and y + 1 where x and y are even integers. Multiplying the two gives us:
(x + 1) * (y + 1)
= x * y + x * 1 + 1 * y + 1 * 1
= xy + x + y + 1
We know that x * y will be even because x and y are also even and the sum of two even numbers will be even, and we also know that x and y are even and that 1 is odd. Since the sum of even and odd numbers is always odd, the product of any two numbers is always odd.
*NOTE: I put a limitation on x and y in my proof (the limitation was that x and y must be EVEN integers) but you don't have to do that, you could make the odd integers 2x + 1 and 2y + 1 where x and y could be any integer from the set Z like mirai123 did. I simply gave this proof because it was the first thing that came to mind. While mirai123's proof and mine are different, they are still both correct.
