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Okay. Now that weamp;#39;ve introduced this input validity problem, letamp;#39;s work toward a situation, which is going to lead towards a programming problem for you where you have to solve this kind of problem. The specific problem that weamp;#39;re going to look at is generating valid credit card numbers. And so you might ask the question, amp;quot;Why would we care about generating valid credit card numbers?amp;quot; and the assumption here is that you are working on some software under test whose input domain is valid credit card numbers. And so your software under test is probably doing something like processing payments and its output is going to be something like completed transactions. So now how are you going to test this? Well, one thing youamp;#39;re going to do is collect some credit cards that you have and that your friends have. And so youamp;#39;ll have a variety of Mastercard and American Express and other kinds of credit cards. Youamp;#39;re going to run it th