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#a17abd15-1762-4fbb-aaae-322bc1612ba1中等解答题集合新定义问题集合与常用逻辑用语

18.定义全集UU的子集AA的特征函数fA(x)={1,xA0,xUAf_{A}(x)=\left\{\begin{array}{l}{1,x\in A}\\ {0,x\in {\complement }_{U}A}\end{array}\right.,这里UA\complement _{U}A表示AA在全集UU中的补集,那么对于集合AABUB\sube U,下列所有正确说法的序号是 [ (1)(2)(4) ].
(1)ABfA(x)fB(x)A\sube B\Rightarrow f_{A}(x)\leqslant f_{B}(x);(2)fUA(x)=1fA(x){f}_{{\complement }_{U}A}(x)=1-f_{A}(x);(3)fAB(x)=fA(x)+fB(x)f_{A\bigcup B}(x)=f_{A}(x)+f_{B}(x);(4)fAB(x)=fA(x)fB(x)f_{A\bigcap B}(x)=f_{A}(x)\cdot f_{B}(x)