Given the true statements: (1) If $a$ is greater than $b$, then $c$ is greater than $d$ (2) If $c$ is less than $d$, then $e$ is greater than $f$. A valid conclusion is:
$\textbf{(A)}\ \text{If }{a}\text{ is less than }{b}\text{, then }{e}\text{ is greater than }{f}\qquad \\ \textbf{(B)}\ \text{If }{e}\text{ is greater than }{f}\text{, then }{a}\text{ is less than }{b}\qquad \\ \textbf{(C)}\ \text{If }{e}\text{ is less than }{f}\text{, then }{a}\text{ is greater than }{b}\qquad \\ \textbf{(D)}\ \text{If }{a}\text{ is greater than }{b}\text{, then }{e}\text{ is less than }{f}\qquad \\ \textbf{(E)}\ \text{none of these}$
(A) is not valid because $af$ does not imply $cb$ does imply $c>d$, but the inverse of Statement 2 ($e\le f$) is not necessarily true.
So the answer is $\boxed{\textbf{(E) } \text{None of these}}$.
(Incidentally, the wording of this problem appears to be wrongly assuming that $x\noty$ (and vice versa) when in reality $x$ and $y$ could be equal. However, this does not change the fact that none of the four choices follow logically from the given statements.)