Answer
a. "If $x$ is a real number and $x\gt1$, then $x^{2}\gt{x}$."
b. "Let $x$ be a real number such that $x\gt1$."
"Therefore, for all real numbers $x$, if $x\gt1$, then $x^{2}\gt$$x$.
Work Step by Step
For part (a), we simply incorporate the fact that $x$ is a real number into the hypothesis (the "if" part of the statement). For parts (b) and (c), we need only to note that the proof in question is a proof by generalization from the generic particular (see page 151). Therefore, we begin the proof by asserting that a specific but arbitrary number that satisfies the hypothesis exists, and conclude the proof by restating what we set out to prove. For more on this, see example 4.1.8 under the heading "Getting Proofs Started" on page 158.
