1. For $a \in \mathbf{R}$, the sets are:
$$
\begin{array}{l}
M=\{x|| x \mid<a, x \in \mathbf{R}\}, \\
N=\{x \mid-a<x<a, x \in \mathbf{R}\} .
\end{array}
$$

Then the relationship between $M$ and $N$ is ( ).
(A) $M \supset N$
(B) $M \subset N$
(C) $M=N$
(D) Cannot be determined, depends on the sign of $a$
-、1.C.
When $a>0$, it is well known that $|x|<a \Leftrightarrow -a<x<a$, so $M=$ $N \neq \varnothing$. When $a \leqslant 0$, by the non-negativity of the absolute value, we know that $M=\varnothing$. And from $0 \leqslant -a<x<a \leqslant 0$ which is a contradiction, we know that $N=\varnothing$. Therefore, $M=N$.