设 $A, B, C$ 是三个随机事件, $0 < P(A) < 1, P(A C)>0$, 则下列说法错误的是
A
$\mathrm{P}(A B)+\mathrm{P}(A C)+\mathrm{P}(B C) \geqslant \mathrm{P}(A)+\mathrm{P}(B)+\mathrm{P}(C)-1$
B
$\mathrm{P}(A B)+\mathrm{P}(A C) \geqslant \mathrm{P}(A)+\mathrm{P}(B C)-1$
C
$\mathrm{P}(B \mid A)>\mathrm{P}(B \mid A C)$
D
$\mathrm{P}(B \mid A)+\mathrm{P}(B \mid \bar{A}) \geqslant \mathrm{P}(B)$
E
F