1. Let set $A=\left\{x \mid x=a^{2}+1, a \in \mathbf{N}_{+}\right\}, B=\left\{y \mid y=b^{2}-4 b+5, b \in\right.$ $\left.\mathbf{N}_{+}\right\}$, then the correct relationship among the following is ( ).
A. $A=B$
B. $A \supset B$
C. $A \subset B$
D. $A \cap B=\varnothing$
1. C. $y=b^{2}-4 b+5=(b-2)^{2}+1$, when $b=2$, $b-2=0$, so $1 \in B$, but $1 \notin A$.