Are you sure there's no implied information, or something they said before about table legs and what support they offer? For example, in my statics class, the prof always drew the supports in a way that we would know exactly what support reactions existed at the support so that she wouldn't have to write it out in the question every time.
I've attached a free body diagram of my interpretation. Even my free body diagram makes some assumptions, and it's still indeterminate. You only have 2 useful equations, but you have three unknowns. The thing is, there's absolutely no reason, based on the information you've given, to assume that the moment at B is zero, so adding that diagram kills it even more. Adding horizontal forces to both legs doesn't really change anything, since they just cancel each other out. That system is indeterminate based on my FBD unless one of the forces/moments shown is zero. Since it seems more reasonable that a table leg would be providing an upward force as opposed to a moment and no upward force, it would make sense to me that the moment at A is zero. That's a pretty poor argument, though, even if it ends up being right.
