I was stumped on product B and C for this problem. There are two pictures attached, the first is the problem, the second is the mechanism that the professor proposed. My concern is that base deprotonating the carbon(s) adjacent to the carbocation. The conditions he specified for the reaction are "acid catalyst" with no water. The elimination product (E1) that he proposes requires a base, but ignoring the fact that no other reagents are indicated, how can a base (even a weak one) exist in acidic conditions in the absence of water (which would form the transdiol product)? Am I crazy??