The argument in the stimulus is flawed because it concludes that because one of the alternatives is false, the other must be true, thus ignoring the possibility that both could be false - neither of the suspects committed the burglary. (D) exhibits a similarly flawed reasoning. Baxim is considering moving their headquarters to A v B, and decided against A, thus it must be B. This argument ignores the fact that Baxim could keep its headquarters at its current location and move to neither of these places. (E) looks similar but it is actually a valid argument. There are only two candidates in the mayoral race - S v G. One of them definitely has to win the race by definition, thus if we know that S has little chance of winning - ~S, we can conclude that G will become the mayor.