The following statement is true. (Note that you do not need to understand the statement in order to be able to do this exercise.) For every real number x, if x > 1 then x2 > x. (a) Fill in the blanks to rewrite the statement with the quantification implicit. If ---Select--- , then ---Select--- . (b) What could be the first sentence of a proof (the "starting point")? Suppose x is any real number such that x > 1. Suppose x = 1. Suppose x is any positive real number. Suppose x is any real number such that x2 > x. Suppose x = 2. What could be the last sentence of a proof (the "conclusion to be shown")? Therefore x2 > x. Therefore x2 < x. Because x = 1, x2 = 1, thus x2 = x. Because x = 2, x2 = 4, thus x2 > x. Therefore x > 1