[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 if [math]A[/math] and [math]B[/math] are independent so are

• [math]A[/math] and [math]\tilde B[/math].
• [math]\tilde A[/math] and [math]\tilde B[/math].