An event A is said to attract event B if P(B | A) > P(B) and repel B if P(B | A) < P(B). (This refines the notion of dependent events by specifying whether A makes B more likely or less likely to occur.)
a. Show that if A attracts B, then A repels B′.
b. Show that if A attracts B, then A′ repels B.
c. Prove the Law of Mutual Attraction: event A attracts event B if, and only if, B attracts A.