Chapter 12, Problem 25CRP

Suppose you needed to find out if anyone in a group of people had a birthday on a particular date. One approach would be to ask the members one at a time. If you took this approach, the occurrence of what event would tell you that there was such a person? What event would tell you that there was no such person? Now suppose that you wanted to find out if at least one of the positive integers has a particular property and you applied the same approach of systematically testing the integers one at a time. If, in fact some integer has the property, how would you find out? If, however, no integer has the property, how would you find out? Is the task of testing to see if a conjecture is true necessarily symmetric with the task of testing to see if it is false?