Why? What’s the logic involved?
The correct answer is July 16, but I get torn up at one point.
Since Albert and Bernard don’t know the same information but Albert knows that Bernard doesn’t know a particular piece of information, you can assume that any information that does not share a month or date can be eliminated.
For instance, there’s only one instance of 19, so May 19 is out. Likewise, there’s only one instance of 18, so June 18 is out. This also eliminates June 17 since only one June would be left and that eliminates August 17 since there would be no other 17.
That leaves May 15 & 16, July 14 & 16, and August 14 & 15. Since there are two instances of each month and two instances of each date, I’m left wondering how they get down to July 16, but that is the correct answer.