3. Determine the truth value of each of the statements below. Justify your answer. The domain for $x$ in
all cases is the set
$S = \{-3, -\frac{1}{3}, 0, \frac{1}{3}, 3\}$
[8 points] (Most relevant reading: BoP 2.7)
(a) $\exists x \in S, x^3 \le x$.
(b) $\forall x \in S, x^3 \le x$.
(c) $\exists n \in \mathbb{N}, \forall x \in S, |\frac{x}{n}| > 0.1$.
(d) $\forall n \in \mathbb{Z} - \{0\}, \exists x \in S, |\frac{x}{n}| > 0.1$.