(15) 1 Represent the set using the roster method: $A=\left\{x \left\lvert\, x=\frac{a}{|a|}+\frac{|b|}{b}+\frac{|c|}{c}+\frac{a b c}{|a b c|}\right., a, b\right.$, $c \in \mathbf{R}, a b c \neq 0\}$ is . $\qquad$
Since $a, b, c \in \mathbf{R}$, and $a b c \neq 0$, the possible values of $a, b, c$ are: all negative, one positive and two negative, two positive and one negative, and all positive.
When $a, b, c$ are all negative, $\frac{a}{|a|}+\frac{|b|}{b}+\frac{|c|}{c}+\frac{a b c}{|a b c|}=-4$;
When $a, b, c$ are one positive and two negative, without loss of generality, assume $a>0, b<0, c<0$, then
$$
\frac{a}{|a|}+\frac{|b|}{b}+\frac{|c|}{c}+\frac{a b c}{|a b c|}=0 \text {; }
$$

When $a, b, c$ are two positive and one negative, without loss of generality, assume $a>0, b>0, c<0$, then
$$
\frac{a}{|a|}+\frac{|b|}{b}+\frac{|c|}{c}+\frac{a b c}{|a b c|}=0 \text {; }
$$

When $a, b, c$ are all positive, $\frac{a}{|a|}+\frac{|b|}{b}+\frac{|c|}{c}+\frac{a b c}{|a b c|}=4$.
Therefore, $A=\{-4,0,4\}$.
Key points for solving the problem: When using the enumeration method to represent a set, be careful not to repeat or omit any elements, and understanding sets is also an important basic skill.