Which of the following is the negation of the statement: For all $x$ of a certain set, $x^2>0$?
$\textbf{(A)}\ \text{For all x}, x^2 0\qquad \\ \textbf{(D)}\ \text{For some x}, x^2>0\qquad \textbf{(E)}\ \text{For some x}, x^2 \le 0$
In general, the negation of a universal ("for all") quantifier will use an existential ("there exists") quantifier, and negate the statement inside.  
In this case, we change the "For all" to "There exists", and negate the inner statement from $x^2 > 0$ to $x^2 \le 0$.
So, the negation of the original statement is "There exists an $x$ such that $x^2 \le 0$".  Exactly one of the two statements is true, but not both.  This is the same as answer $\boxed{\textbf{(E)}}$.