10. 已知集合 $A=\left\{\alpha \mid k \cdot 180^{\circ}+30^{\circ}<\alpha<k \cdot 180^{\circ}+90^{\circ}, k \in \mathbf{Z}\right\}$, 集合 $B=\left\{\beta \mid k \cdot 360^{\circ}-45^{\circ}<\beta<k \cdot 360^{\circ}\right.$ $\left.+45^{\circ}, k \in \mathbf{Z}\right\}$. 求:

(1) $A \cap B$; (2) $A \cup B$.
由题意可画图.

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由图可知,

$A \cap B=\left\{\theta \mid 30^{\circ}+k \cdot 360^{\circ}<\theta<45^{\circ}+k \cdot 360^{\circ}, k \in \mathbf{Z}\right\}$,

$A \cup B=\left\{\gamma \mid k \cdot 360^{\circ}-45^{\circ}<\gamma<k \cdot 360^{\circ}+90^{\circ}\right.$ 或 $\left.k \cdot 360^{\circ}+210^{\circ}<\gamma<k \cdot 360^{\circ}+270^{\circ}, k \in \mathbf{Z}\right\}$.