How can I write a function that takes an array of integers and returns true if their exists a pair of numbers whose product is odd?

What are the properties of odd integers? And of course, how do you write this function in Java? Also, maybe a short explanation of how you went about formulating an algorithm for the actual implementation.

Yes, this is a function out of a textbook. No, this is not homework—I'm just trying to learn, so please no "do your own homework comments."