Prediction markets provide a mechanism for using groups of people to determine the probability of events. We ask whether these probability estimates, for logically related events, exhibit the irrationalities often found in individual judgments. In particular, we explore combinations of markets that provide tests of classic conjunction and disjunction fallacies. Across a number of markets, asking about a wide variety of events, we find a few interesting violations of probability theory, but mostly rational adherence. We discuss our exploratory analyses in terms of the relationship between group and individual probability estimation, and the effectiveness of prediction markets.