1. （5 分）已知集合 $A=\{x \mid x<2\}, B=\{x \mid 3-2 x>0\}$, 则（）
Gaokao · Math · previous-year question
- A.$A \cap B=\left\{x \mid x<\frac{3}{2}\right\}$correct
- B.$A \cap B=\varnothing$
- C.$A \cup B=\left\{\mathbf{x} \mid \mathbf{x}<\frac{3}{2}\right\}$
- D.$A \cup B=R$
Answer
A. $A \cap B=\left\{x \mid x<\frac{3}{2}\right\}$
Explanation
解: $\because$ 集合 $A=\{x \mid x<2\}, B=\{x \mid 3-2 x>0\}=\left\{x \mid x<\frac{3}{2}\right\}$, $\therefore A \cap B=\left\{x \mid x<\frac{3}{2}\right\}$, 故 A 正确, $B$ 错误; $A \cup B=\{x|| x<2\}$, 故 C, D 错误; 故选: A.
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