[math] \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}[/math]

Prove that [math]A[/math] and [math]B[/math] are mutually attractive if and only if [math]P(B|A) \gt P(B|\tilde A)[/math].