Skill/Comprehending and producing sentences with single quantifiers

=Definition= Examples of sentences with single quantifiers include:
 * $\forall n \in \ZZ, n^3 + 1 > n$.
 * $\exists x \in \RR, x^2 < x$.

Students who are familiar with high-school algebra, as well as the meaning of the quantifiers and the symbols $\ZZ$ and $\RR$, should comprehend these sentences, and determine whether they are true or false.

In addition, students who are familiar with high-school algebra should be able to write true and syntactic sentences, to express facts they know about real numbers and whole numbers. For example, a student who can produce sentences with single quantifiers can make the transition from the first sentence to the second below:
 * For large enough real numbers $x$, $2^x > x^4$.
 * $\exists M \in \RR, x > M \Rightarrow 2^x > x^4$.