Gane Show Shenanigans: Monty Hall Meets Mathematical Logic

The classical (now famous) Monty Hall problem entails that a hypothetical game show contestant be presented three doors and told that behind one door is a car and behind the other two are goats. The contestant is to pick a door, and then the host (Monty) is to open a different door which houses a goat. The contestant is then given the option of keeping the door she chose or changing her selection, after which Monty opens the chosen door and the contestant wins the prize which lies behind it. In this note, we consider two logic-themed variants of this problem.