1. Let set $A=\{(x, y) \mid x+y=1\}, B=\left\{(x, y) \mid x^{2}+y^{2}=2\right\}, C=A \cap B$, then the number of subsets of set $C$ is $\qquad$ .
Since the distance $d$ from the center of the circle $(0,0)$ to the line $x+y=1$ is $d=\frac{1}{\sqrt{2}}<\sqrt{2}$, then $|C|=2$. Therefore, the number of subsets of set $C$ is 4.