(5分)设全集$U=\{-2$,$-1$,0,1,2,$3\}$,集合$A=\{-1$,$2\}$,$B=\{x\vert x^{2}-4x+3=0\}$,则$\complement _{U}(A\bigcup B)=($ ) A.$\{1$,$3\}$ B.$\{0$,$3\}$ C.$\{-2$,$1\}$ D.$\{-2$,$0\}$ 分析:求解一元二次方程化简$B$,再由并集与补集运算得答案. 解答:解:$\because B=\{x\vert x^{2}-4x+3=0\}=\{1$,$3\}$,$A=\{-1$,$2\}$, $\therefore A\bigcup B=\{-1$,1,2,$3\}$, 又$U=\{-2$,$-1$,0,1,2,$3\}$, $\therefore \complement _{U}(A\bigcup B)=\{-2$,$0\}$. 故选:$D$. 解答:本题考查交、并、补集的混合运算,是基础题.
|