1. If $x, y \in R$, then the relationship between the sets of real numbers $P=\left\{s \mid s=x^{2}+3 x\right.$ $+1\}$ and $Q=\left\{t \mid t=y^{2}-3 y+1\right\}$ is ( ).
(A) $P \cap Q=\varnothing$
(B) $P \subset Q$
(C) $P \supset Q$
(D) $P=Q$
1. (D)
$$
\because P=\left\{s \left\lvert\, s=\left(x+\frac{3}{2}\right)^{2}-\frac{5}{4}\right.\right\} \text {, }
$$
$\therefore$ The range of values for the element $s$ in $P$ is $\left[-\frac{5}{4},+\infty\right)$. $X \because Q=\left\{t \left\lvert\, t=\left(y-\frac{3}{2}\right)^{2}-\frac{5}{4}\right.\right\}$,
$\therefore$ The range of values for the element $t$ in $Q$ is $\left[-\frac{5}{4},+\infty\right)$. Therefore, $P=Q$.