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
$P (A B)+ P (A C)+ P (B C) \geqslant P (A)+ P (B)+ P (C)-1$
B
$P (A B)+ P (A C) \geqslant P (A)+ P (B C)-1$
C
$P (B \mid A)> P (B \mid A C)$
D
$P (B \mid A)+ P (B \mid \bar{A}) \geqslant P (B)$
E
F