1. If n + 1 integers are chosen from the set {1,2, 3, ......, 2n} where n is a positive integer, must at least one of them be odd? must one of them be even? Explain why. 2. How many integers must be selected from the set of integers from 2 through 40, to ensure there are at least two integers with a common divisor greater than 1. 3. A certain mathematics class has 40 students. All the students in the class are known to be from 17 through 34 years of age. You want to make a bet that the class contains at least x students of the same age. How large can you make x and still be sure to win your bet?