1) Complete the following exhaustive proof of:

If a positive integer x is less than 10, then x2 < 200.

List positive integers x < 10 List corresponding x2 Is x2 < 200?

    

    

    

    

    

    

    

    

    

2) Use a direct proof to show: "If x is an odd integer and y is an even integer, then x + y is odd."

3) Use proof by contraposition to show: "If x2 is even, then x is even."

4) Use proof by contradiction to show: "If x2 is even, then x is even."

5) Prove that 20 + 21 + 22 + 23 + . . . + 2n = 2n + 1 - 1 for all nonnegative integers n.