Chapter 8.3, Problem 76E

Show that if $A$ and $B$ are events with nonzero probabilities in a sample space $S$ and either

$P\left(A\left|B\right.\right)=P\left(A\right)\text{or}P\left(B\left|A\right.\right)-P\left(B\right)$, then events $A$ and $B$ are independent.