1. Let $M=\{x \mid x=n, n \in \mathbf{Z}\}, N=\left\{x \left\lvert\, x=\frac{n}{2}\right., n \in \mathbf{Z}\right\}, P=$ $\left\{x \left\lvert\, x=n+\frac{1}{2}\right., n \in \mathbf{Z}\right\}$, which of the following is correct? ( ).
A. $N \subset M$
B. $N \subset P$
C. $N=M \cup P$
D. $N=M \cap P$
1. C. $x=n=\frac{2 n}{2}, x=n+\frac{1}{2}=\frac{2 n+1}{2}, x=\frac{n}{2}$.