下列选项中的两个集合相等的有
$\text{A.}$ $P=\{x \mid x=2 n, n \in \boldsymbol{Z}\}, Q=\{x \mid x=2(n+1), n \in \boldsymbol{Z}\}$
$\text{B.}$ $P=\left\{x \mid x=2 n-1, n \in \boldsymbol{N}_{+}\right\}, Q=\left\{x \mid x=2 n+1, n \in \boldsymbol{N}_{+}\right\}$
$\text{C.}$ $P=\left\{x \mid x^2-x=0\right\}, Q=\left\{x \left\lvert\, x=\frac{1+(-1)^n}{2}\right., n \in \boldsymbol{Z}\right\}$
$\text{D.}$ $P=\{x \mid y=x+1\}, Q=\{(x, y) \mid y=x+1\}$